SEMINARI
DI
GEOMETRIA

organizzati congiuntamente dai Dipartimenti di Matematica dell' Universita' degli Studi
e del Politecnico di Milano

Coordinatori: Enrico Schlesinger ed Elisabetta Colombo

Per ulteriori informazioni rivolgersi a
 24/11/22 ore: 11:00 Lorenzo Venturello (Università degli Studi di Pisa) Aula Seminari III piano Two graph polytopes Abstract:In this talk I will focus on two integral convex polytopes one can construct from a graph: symmetric edge polytopes and cosmological polytopes. Both constructions have been introduced and studied in the context of physics, and the former plays a key role also in the study of finite metric spaces and optimal transport. The general goal is to understand how interesting geometric invariants of these polytopes (their Ehrhart theory, volume, triangulations) are related to the combinatorics of the underlying graph. In the first part I will present a conjecture due to Ohsugi and Tsuchiya on a numerical invariant called the $h^*$-vector of symmetric edge polytopes, and present partial results obtained in a joint work with Alessio D’Alì, Martina Juhnke-Kubitzke and Daniel Köhne. In the second part I will focus on cosmological polytopes. In a joint work (in progress) with Martina Juhnke-Kubitzke and Liam Solus we show that all these polytopes have a regular unimodular triangulation. As a result we compute the volume of the cosmological polytope of the cycle graph. 23/11/22 ore: 17:00 Mark Elin (Braude College of Engeneering, Israel) On line Filtration of generators and an inverse Fekete--Szego problem Abstract:In this talk, based on joint works, we present some results connecting dynamic system with geometric function theory. In the first part of the talk, we study the problem of characterizing membership of normalized holomorphic functions of the disk to the class of infinitesimal generators and some its subclasses as well as dynamical properties of generated semigroups. Presenting results include analytic extension in the semigroup parameter and the uniform convergence. Our approach is based on so-called filtrations' of the class of infinitesimal generators. In the second part we introduce and study a question that can be interpreted as an inverse Fekete-Szego problem'. This problem links to the first part of the talk. We introduce new filtration classes using a suitable non-linear differential operator and establish certain properties of these classes. Sharp upper bounds of the absolute value of the Fekete--Szego functional over some filtration classes are found. We also present open problems for further study. 10/11/22 ore: 11:00 Martin Kalck (Freiburg, Germania) Aula Seminari III piano Derived categories of singular projective varieties and finite dimensional algebras Abstract:We will describe recent progress on describing derived categories of coherent sheaves for certain singular projective varieties in terms of derived categories of finite dimensional algebras, which are typically noncommutative. This is based on ongoing joint works with Yujiro Kawamata & Nebojsa Pavic and with Carlo Klapproth, Nebojsa Pavic & Evgeny Shinder. 27/10/22 ore: 11:30 Lisa Nicklasson (Università degli Studi di Genova) Aula Seminari III piano Ideals arising from Bayesian networks Abstract:A Bayesian network is a statistical model which can be presented graphically by a directed acyclic graph. The nodes in the graph are discrete random variables, and the edges encode dependencies between the variables. Bayesian nets can also be described algebraically as varieties of homogeneous prime ideals. In this talk we will discuss connections between algebraic properties of such ideals and combinatorial properties of the graphs. In particular, we would like to understand when the variety is toric and when the ideal is quadratic. 19/10/22 ore: 17:00 Swanhild Bernstein (TU Bergakademie Freiberg) On line Basic Clifford q-Calculus 21/09/22 ore: 17:00 Bingyuan Liu (University of Texas Rio Grande Valley ) On line The Diederich-Fornaess index and the dbar-Neumann problem Abstract:A domain $\Omega$ in $\mathbb C^n$ is said to be pseudoconvex if $-\log(-\delta(z))$ is plurisubharmonic in $\Omega$, where $\delta$ is a signed distance function of $\Omega$. The study of global regularity of the dbar-Neumann problem on bounded pseudoconvex domains is dated back to the 1960s. However, a complete understanding of the regularity is still absent. On the other hand, the Diederich-Fornaess index was introduced in 1977 originally for seeking bounded plurisubharmonic functions. Through decades, enormous evidence has indicated a relationship between global regularity of the dbar-Neumann problem and the Diederich-Fornaess index. Indeed, it has been a long-lasting open question whether the trivial Diederich-Fornaess index implies global regularity. In this talk, we will introduce the backgrounds and motivations. We will also answer this open question by a recent result of Straube and me. 27/07/22 ore: 17:00 Nikolaos Chalmoukis (Saarland University) On line Exceptional sets for Hardy Sobolev spaces in several complex variables Abstract:The class of holomorphic Hardy Sobolev spaces in the unit ball of $\mathbb C^n$ is a family of spaces including the Hardy, Drury Arveson, Bergman and Dirichlet space. In this talk we will focus on questions regarding exceptional sets both from function theoretic and a functional analytic perspective. These two approaches have led to the past in two different notions of exceptional sets. From the point of view of function theory, exceptional sets are sets where a function in the corresponding Hardy Sobolev space fails to have admissible limits and can be characterized as null sets for some appropriately defined capacity. While from the functional analysis perspective null sets, called totally null sets, play the role of Lebesgue measure zero sets in the Sz.-Nagy-Foias $H^\infty(D)$ functional calculus. The problem of bridging these two approaches will be the main topic of the talk. The talk is based on joint work with Michael Hartz. 15/06/22 ore: 17:00 Kamal Diki (Chapman University) On line Fueter mapping theorem and generalized Appell polynomials in the poly-analytic setting Abstract:The Fueter mapping theorem is a fundamental result in quaternionic analysis relating slice hyperholomorphic functions and Fueter regular ones. The action of the Fueter map on quaternionic monomials leads to an interesting class of functions forming an Appell system with respect to the hypercomplex derivative. In this talk I will present two extensions of the Fueter map in the case of polyanalytic functions of a quaternionic variable. The first map is built upon a suitable global operator with non-constant coefficients allowing to construct Fueter regular functions starting from poly-slice hyperholomorphic ones. The second map allows to construct polyanalytic Fueter regular functions. Based on this second construction we introduce and study the main properties of a new family of Generalized-Appell polynomials which are poly-Fueter regular. I will discuss also how the polyanalytic Fueter maps act on a poly slice hyperholomorphic Bargmann transform. This gives rise to two integral transforms in the Fueter regular and polyanalytic Fueter regular setting. 18/05/22 ore: 17:30 Anne-Katrin Gallagher (Oklahoma State University) On line On plurisubharmonic defining functions Abstract: I will present results pertaining to the question of existence of plurisubharmonic defining functions for smoothly bounded, pseudoconvex domains. This talk is based on joint work with Tobias Harz. 12/05/22 ore: 14:00 Andreas Krug (Leibniz Universität Hannover, Germania) Aula Seminari del terzo piano Compactified Jacobians of non-integral curves and Lagrangian fibrations Abstract:I report on joint work in progress with Adam Czaplinski, Manfred Lehn, and Sönke Rollenske. We describe moduli spaces of stable sheaves, which are generically line bundles on a certain class of non-integral curves, which we call extended ADE curves. This class generalises the non-integral fibres of elliptic fibrations. The main motivation is that our moduli spaces occur as general singular fibres of Lagrangian fibrations. 06/05/22 ore: 14:00 Alberto Debernardi Pinos (Università di Aveiro) Aula Seminari del terzo piano Riesz basis of exponentials for convex polytopes with symmetric faces Abstract:We will discuss a joint result with Nir Lev, which states that for any convex and centrally symmetric polytope $\Omega\subset \mathbb{R}^d$, whose faces of all dimensions are also centrally symmetric, there exists a Riesz basis of exponential functions for $L^2(\Omega)$. This result extends previously known statements in this direction due to Lyubarskii and Rashkovskii, and also due to Walnut ($d=2$), and by Grepstad and Lev (in arbitrary dimensions), where the same conclusion is obtained under the additional assumption that all the vertices of $\Omega$ lie in the lattice $\mathbb{Z}^d$. 20/04/22 ore: 17:00 Uwe Kaehler (University of Aveiro) On line e Aula Seminari del terzo piano Global pseudo-differential operator calculus over spin groups Abstract:In this talk we present a method to construct a global symbol calculus of pseudo-differential operators on spin groups in the sense of Ruzhansky-Turunen-Wirth, focussing on the special case Spin(4). Using representations of Spin(4) we construct a group Fourier transform and establish the calculus of left-invariant differential operators and of difference operators on the group Spin(4). Afterwards we apply this calculus to give criteria for the subellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of first and second order globally hypoelliptic differential operators are given, including some that are locally neither invertible nor hypoelliptic. 16/03/22 ore: 17:00 Leandro Arosio (Università di Roma 2) On line Horospheres in several complex variables Abstract: A horocycle in the unit disk of the complex plane is a euclidean disk which is internally tangent to a point p of the boundary of the disk. Horocycles are limits of Poincaré balls as the center moves towards the point p while the radius grows suitably. The classical Julia lemma is a boundary version of the Schwarz lemma which shows that horocycles are useful to understand the behaviour of a holomorphic self-map of the disk near a point of the boundary. In this talk we deal with the generalization of this concept to several complex variables: horospheres. The existence of horospheres in bounded strongly convex domains of C^n was proved by Abate in 1988 using Lempert’s theory of complex geodesics. It is difficult to generalize such proof to bounded strongly pseudoconvex domains, which is the natural class of domains to study in this context. In this talk I will show how to obtain this generalization following a different route, that is, proving that the horofunction compactification of the domain is topologically equivalent to its Gromov compactification. This is a joint work with Matteo Fiacchi, Sébastien Gontard, and Lorenzo Guerini. 24/02/22 ore: 14:00 Alessandro Oneto (Università degli Studi di Trento) Aula seminari del terzo piano On the strength of homogeneous polynomials Abstract:The strength of a homogeneous polynomial is the smallest length of an additive decomposition as sum of reducible forms. It is called slice rank if we additionally require that the reducible forms have a linear factor. Geometrically, the slice rank corresponds to the smallest codimension of a linear space contained in the hypersurface defined by the form. Due to this relation, it is well-known and easy to compute the value of the general slice rank and also to show that the set of forms with bounded slice rank is Zariski-closed. In this talk, I will present the following results from recent joint works with A. Bik, E. Ballico and E. Ventura: (1) the set of forms with bounded strength is not always Zariski-closed: this is an asymptotic result in the number of variables proved by using the theory of polynomial functors; (2) for general forms, strength and slice rank are equal: this is proved by showing that the largest component of the secant variety of the variety of reducible forms is the secant variety of the variety of forms with a linear factor. 16/02/22 ore: 17:00 Alain Yger (Université de Bordeaux) On line Revisiting syzygies, hence division or interpolation problems, in terms of residue and principal value currents Abstract: A joint paper I wrote together with M. Passare and August Tsikh in 2000 (ideas there coming from my unfortunately last joint paper with Carlos Berenstein in 1998) inspired since then the construction of what reveals to be a very powerful method to attack interpolation or division problems in C^n or P^n(C) (also on Stein manifolds) by solving them through explicit closed formulae. The beautiful idea which was introduced by Mats Andersson since 2004 consists in the following: attach to any generically exact complex of hermitian bundles over a complex analytic space both a Principal Value current and a residue current, the last one precisely encoding the lack of exactness of the complex of holomorphic bundles one started with. Time has now come, despite the technicity inherent to such construction, to popularize such tool facing general questions such as Hilbert's Nullstellensatz, the surprising (and curiously not so-well known) Briancon-Skoda theorem (even in the polynomial setting), Euler-Ehrenpreis-Palamodov Fundamental Principle, or spectral synthesis problem in (adhoc) weighted algebras of entire functions. I will try to explain this in general terms, avoiding as far as I can technicalities by cheating a little, and will illustrate with few concrete examples the novelty and efficiency of such approach. The recent monograph I wrote with Alekos Vidras about such developments of multivariate residue calculus in the past decades (which has been accepted in the AMS Mathematical Surveys and Monographs collection) inspired this lecture. Since the concept of Bochner-Martinelli kernel appears to be the keystone in such construction, I will make some digression about its use by R. Fueter in univariate quaternionic calculus, as an invitation to transpose the machinary of multivariate Principal Values and residue calculus to the noncommutative frame of H^1. 22/01/22 ore: 14:30 Viola Siconolfi (Università di Pisa) Aula seminari del sesto piano Ricci curvature, graphs and Coxeter groups Abstract:I will talk about a notion of curvature for graphs introduced by Schmuckenschläger which is defined as an analogue of Ricci curvature. This quantity can be computed explicitly for various graphs  and allows to find bounds on the spectral gap of the graph and isoperimetric-type inequalities. I will present some general results on the computation of the discrete Ricci curvature of any locally finite graph. I will then focus on graphs associated with Coxeter groups: Bruhat graphs, weak order graphs and Hasse diagrams of the Bruhat order 19/01/22 ore: 17:00 Milton Ferreira (Polytechnic of Leiria (Portugal)) On line Symbol calculus of pseudo-differential operators on Spin(4) Abstract: During the last decade, a new and full symbol calculus over compact groups was developed by M. Ruzhansky, V. Turunen, and J. Wirth which represents a non-commutative extension of the classical Kohn-Nirenberg quantization. This calculus has several advantages over the classic principle calculus of L. Hormander, which is based on the notion of the symbol via localizations, such as the characterization of global and local hypoellipticity. In this seminar, we present a full symbol calculus of pseudo-differential operators on the group Spin(4). The essential tools for such calculus are the Spin(4)-representations, its matrix coefficients, recurrence relations, difference operators acting on them, and the Fourier transform on Spin(4). Spin(4)-representations are constructed in the spaces of simplicial harmonic and spinor-valued monogenic polynomials using tools from Clifford analysis. Since Spin(4) is isomorphic to the direct product group of Spin(3) with itself, Spin(4)-representations decompose as the tensor product of Spin(3)-representations. With all the tools in hand, we characterize elliptic and global hypoelliptic pseudo-differential operators in Spin(4), in terms of their matrix-valued full symbols. Some examples of first and second-order globally hypoelliptic differential operators will be shown, in particular, of operators that are locally not invertible nor hypoelliptic but globally are. 15/12/21 ore: 18:00 Irina Markina (University of Bergen, Norway ) On line From Clifford algebras to Heisenberg type Lie algebras Abstract:As it is well known, the Clifford algebras have numerous applications. In the present talk, we will explain how the Clifford algebras and their representation can build two-step nilpotent Lie algebras. They received the name Heisenberg type Lie algebras, due to the fact that the classical Heisenberg algebra is the simplest example in this construction. A special class of Heisenberg type Lie algebras was introduced by A. Kaplan in 1980 to study hypoelliptic partial differential operators and their fundamental solutions. The Heisenberg type Lie algebras admit rational structural constants, that lead to the existence of lattices on the corresponding Lie groups according to the Malcev theorem. The factor of Heisenberg type Lie groups by the lattices gives rise to a chain of examples of nilmanifolds that are isospectral but non-diffeomorphic. In the talk, we will explain the construction of the Heisenberg type Lie algebras and give examples. We also will discuss the classification of the constructed Lie algebras and their group of automorphisms. 17/11/21 ore: 17:00 Phillip S. Harrington (University of Arkansas) On line Maximal Estimates in Several Complex Variables Abstract:Complex analysis in one variable is closely tied to the study of harmonic functions. In several complex variables, there is also a second-order PDE that is fundamental to the study of the holomorphic functions: the $\bar\partial$-Neumann problem. In contrast with the one variable case, the boundary condition for the $\bar\partial$-Neumann problem is non-coercive, so solution operators for the $\bar\partial$-Neumann problem gain at most one derivative in the Sobolev scale. Given this constraint, we say that a domain admits maximal estimates if the solution operator for the $\bar\partial$-Neumann problem gains two derivatives in every direction except one. We will see that a large class of domains admit maximal estimates, and many difficult problems in several complex variables are easier to study on such domains. 09/11/21 ore: 14:00 Davide Bolognini (Università Politecnica delle Marche) aula seminari del terzo piano, online su pagina webex del Professor Roberto Notari Sulla congettura di Simon Abstract:La congettura di Simon sulla extendably shellability degli scheletri del simplesso è un problema aperto da trent'anni. Una recente estensione della nozione di cordalità dai grafi agli ipergrafi (motivata dalla ricerca di una caratterizzazione degli ideali monomiali a risoluzione lineare) ha portato vari autori a formulare, in un contesto algebrico, una ulteriore congettura che implica quella di Simon. In questo seminario presento infiniti controesempi a questa congettura più forte. Tempo permettendo proverò a dare un'idea sulle possibili future direzioni di ricerca sul tema. Questo è un lavoro scritto in collaborazione con Bruno Benedetti. 27/10/21 ore: 17:00 Ali Guzman Adan (University of Ghent) On line (seguirà link) The Dirac delta distribution and inversion formulas for the Radon transform in superspace Abstract:In this talk, we approach the problem of inverting the Radon transform in superspace from two different perspectives. The first one relies on the decomposition into plane waves of the super Dirac Delta distribution, provided that the superdimension is not odd and negative. Such a decomposition is obtained by adopting the point of view of hyperfunctions, namely by using the fact that the Dirac delta is a suitable boundary value of the super Cauchy kernel. In the cases of negative and even superdimension, the obtained formulas no longer resemble the structure of the classical plane wave decompositions in m real dimensions. In turn, the explicit inversion formulas obtained for the super Radon transform in these cases show important differences with the classical case. On the other hand, we show how to invert the super Radon transform using the classical approach, i.e. by composing the dual Radon transform with a certain power of the super Laplace operator. This approach yields a unified inversion formula that is valid for all possible integer values of the superdimension. The proof of this result comes along with the study of fractional powers of the super Laplacian, their fundamental solutions, and the plane wave decompositions of super Riesz kernels. This talk is based on joint work with Irene Sabadini and Frank Sommen. 19/10/21 ore: 15:00 Paolo Sentinelli (Politecnico di Milano) Aula seminari MOX VI piano, online su pagina webex di Roberto Notari Stratificazioni di incidenza Abstract:Introdurremo la nozione di stratificazione di incidenza di una varietà proiettiva. Esempi classici di strati di incidenza sono le varietà di Schubert e gli strati matroidali delle grassmanniane, le varietà di Schubert e gli strati matroidali nelle varietà delle bandiere. Nei casi in cui valga una proprietà di massimalità matroidale, la stratificazione di incidenza dà un insieme di generatori del gruppo di Chow della varietà. We introduce the notion of incidence stratification of a projective variety. Classical examples of incidence strata are Schubert varieties and matroidal strata in Grassmannians, Schubert varieties and matroidal strata in flag varieties. In case a matroidal maximality property holds, the incidence stratification gives a set of generators for the Chow group of the variety. 15/09/21 ore: 17:00 Marco Peloso (Università degli Studi di Milano) https://polimi-it.zoom.us/j/81442277519 Holomorphic function spaces on homogeneous Siegel domains Abstract: Goal of this talk is to present some recent progress in the theory of holomorphic function spaces on homogenous Siegel domains of Type II. These domains are unbounded realisation of the homogeneous bounded domains and include the tube domains over homogeneous cones as a particular case. We first describe the structure and geometrical properties of such domains. Second, we introduce some classes of holomorphic function spaces, including the weighted Bergman spaces, and describe their boundary behaviour. Finally, we concentrate on the boundedness of the Bergman projections, presenting some recent results and open problems. This talk is based on joint work with Mattia Calzi. 21/07/21 ore: 18:00 Malik Younsi (University of Hawaii) On line Holomorphic motions, analytic capacity and conformal welding Abstract:The notion of a holomorphic motion was introduced by Mané, Sad and Sullivan in the 1980's, motivated by the observation that Julia sets of rational maps often move holomorphically with holomorphic variations of the parameters. In the years that followed, the study of the behavior of various set-functions under holomorphic motions became an area of significant interest. For instance, holomorphic motions played a central role in the work of Astala on distortion of Hausdorff dimension and area under quasiconformal mappings. In this talk, I will first review the basic notions and results related to analytic capacity and holomorphic motions, including the extended lambda lemma. I will then present some recent results on the behavior of analytic capacity under holomorphic motions. The proofs involve different notions such as conformal welding, quadratic Julia sets and harmonic measure. This is joint work with Tom Ransford and Wen-Hui Ai. 16/06/21 ore: 17:00 Daniel Alpay (Chapman University) On line Discrete analytic functions and Schur analysis Abstract: We first review both the theory of discrete analytic functions and the main features of Schur analysis (a collection of problems pertaining to functions analytic and contractive in the open unit disk, and with a wide range of applications). Then, we present new connections between the theory of discrete analytic functions and Schur analysis. This allows us to define a new class of problems pertaining to discrete analytic functions. References: D. Alpay, P. Jorgensen, R. Seager, and D. Volok. On discrete analytic functions: Products, Rational Functions, and Reproducing Kernels. Journal of Applied Mathematics and Computing. Volume 41, Issue 1 (2013), Page 393-426. D. Alpay and D. Volok, Discrete analytic functions and Schur analysis. Preprint, 2021. 10/06/21 ore: 14:00 Lukas Braun (Universität Freiburg, Germania) On line Local Cox rings for klt singularities Abstract:In this talk, I will discuss notions of Cox rings for (klt) singularities. We investigate different local models and how the Cox rings behave when changing the model. Finally, we investigate an iteration process for Cox rings and compare the associated covers with covers coming from the local fundamental group. Cordiali saluti, 19/05/21 ore: 17:00 Roman Lavicka (Charles University Prague) On line Fischer decomposition for massless field equations Abstract:Massless field equations are fundamental in particle physics. In Clifford analysis, a version of these equations in Euclidean space of dimension 4 have been studied. In this talk, we shall discuss a recent development on this topic. In particular, for fields with values in a general irreducible spin module, as an analogue of massless field equations we propose the so-called generalized Cauchy-Riemann equations introduced by E. Stein and G. Weiss. Then we describe Fischer decompositions of massless fields up to spin 3/2. This is a joint work with V. Soucek, W. Wang, F. Brackx and H. De Schepper. 13/05/21 ore: 14:00 Fabio Tonini (Università di Firenze) On line Cox rings and Algebraic stacks Abstract:We will discuss the notion of Cox ring for an algebraic stack, which extends the classical notion for varieties, via the language of torsors. We will then present some applications and possible direction of research. 21/04/21 ore: 17:00 Ahmed Sebbar (Chapman University) On line Vieta Formula, Distributions, and Lemniscate Abstract:We give two extensions of the classical Vieta (or Viète) formula. The first extension leads to the classical Fabius function, an infinitely differentiable function that is nowhere analytic. The second extension discusses the corresponding formula for the elliptic curves with complex multiplication $y^2=x^3 -Dx$, $y^2=x^3-D$. 17/03/21 ore: 17:00 Oliver Roth (University of Wuerzburg) On line A new Schwarz-Pick Lemma at the boundary and rigidity of holomorphic maps Abstract:We establish several invariant boundary versions of the (infinitesimal) Schwarz-Pick lemma for conformal pseudometrics on the unit disk and for holomorphic selfmaps of strongly convex domains in CN in the spirit of the boundary Schwarz lemma of Burns-Krantz. Firstly, we focus on the case of the unit disk and prove a general boundary rigidity theorem for conformal pseudometrics with variable curvature. In its simplest cases this result already includes new types of boundary versions of the lemmas of Schwarz-Pick, Ahlfors-Schwarz and Nehari-Schwarz. The proof is based on a new Harnack-type inequality as well as a boundary Hopf lemma for conformal pseudometrics which extend earlier interior rigidity results of Golusin, Heins, Beardon, Minda and others. Secondly, we prove similar rigidity theorems for sequences of conformal pseudometrics, which even in the interior case appear to be new. For instance, a first sequential version of the strong form of Ahlfors' lemma is obtained. As an auxiliary tool we establish a Hurwitz-type result about preservation of zeros of sequences of conformal pseudometrics. Thirdly, we apply the one-dimensional sequential boundary rigidity results together with a variety of techniques from several complex variables to prove a boundary version of the Schwarz-Pick lemma for holomorphic maps of strongly convex domains in $\C^N$ for $N>1$. 17/02/21 ore: 17:00 Hendrik De Bie (Ghent University) On line The Dunkl intertwining operator Abstract:There are two crucial operators in the theory of Dunkl harmonic analysis. The first is the Dunkl transform, which generalizes the Fourier transform. The second is the intertwining operator, which maps ordinary partial derivatives to Dunkl operators. Although some abstract statements are known about the intertwining operator, the explicit formula for classes of reflection groups is generally not known. In recent work Yuan Xu proposed a formula in the case of dihedral groups and a restricted class of functions. We extend his formula to all functions and give a general strategy on how to obtain similar formulas for other reflections groups. This is based on joint work with Pan Lian, available under arXiv:2002.09065 and to appear in J. Funct. Anal. 20/01/21 ore: 17:00 David P. Kimsey (Newcastle University) On line The spectral theorem for a normal operator on a Clifford module Abstract:In this talk we will consider the problem of obtaining a spectral resolution for a densely defined closed normal operator on a Clifford module $\mathcal{H}_n := \mathcal{H} \otimes \mathbb{R}_n$, where $\mathcal{H}$ is a real Hilbert space and $\mathbb{R}_n := \mathbb{R}_{0, n}$ is the Clifford algebra generated by the units $e_1, \ldots, e_n$ with $e_i e_j = -e_j e_i$ for $i \neq j$ and $e_j^2 = -1$ for $j=1,\ldots, n$. We shall see that any densely defined closed normal operator on a Clifford module admits an integral representation which is analogous to the integral representation for a densely defined closed normal operator on a quaternionic Hilbert space (which one may think of as a Clifford module $\mathcal{H}_2$) discovered by Daniel Alpay, Fabrizio Colombo and the speaker in 2014. However, the Clifford module setting sketched above with $n > 2$ presents a number of technical difficulties which are not present in the quaternionic Hilbert space case. In order to prove this result, one needs to slightly generalise the notion of $S$-spectrum to allow for operators which are not necessarily paravector operators, i.e., operators of the form $T =T_0 + \sum_{j=1}^n T_j e_j$. This observation has implications on a generalisation of the $S$-functional calculus and some related function theory which we shall briefly highlight. The main thrust of this talk is based on joint work with Fabrizio Colombo. The work on the $S$-functional calculus is joint work with Fabrizio Colombo, Jonathan Gantner and Irene Sabadini. The work on the related function theory is joint work with Fabrizio Colombo, Irene Sabadini and Stefano Pinton. 16/12/20 ore: 17:00 Alexander Tumanov (University of Illinois at Urbana-Champaign) Dipartimento di Matematica, Politecnico di Milano (on line) Finite jet determination for CR mappings Abstract:A CR mapping is a diffeomorphism between two real manifolds in complex space that satisfies tangential Cauchy-Riemann equations. We are concerned with the problem whether a CR mapping is uniquely determined by its finite jet at a point. This problem has been popular since 1970-s and the number of publications on the matter is enormous. Nevertheles, natural fundamental questions have been open. I will present a solution to a version of the problem and discuss old and recent results. 19/11/20 ore: 14:00 Emanuele Ventura (Universität Bern) Dipartimento di Matematica, Politecnico di Milano (on line, please write to Paolo Lella to obtain the link) Singular curves and osculating spaces Abstract:How bad can singularities of a curve of degree d in projective n-space be? The study of this question is very classical. Even for plane curves, all possible configurations of singularities are only known in low degrees. In higher dimensions, much less is known. In the eighties, Piene and Eisenbud-Harris studied flags of osculating spaces attached to linear series of curves. In this talk, we introduce a gadget (called multifiltration) obtained by combining those flags. We use it to give upper bounds on the arithmetic genus of projective curves in some ranges (reproving a result due to Castelnuovo). We classify all configurations of singularities that can arise when any smooth curve is projected from a linear space of dimension at most two. With these techniques, one can describe the Schubert cycles giving rise to those projections. This is joint work with J. Buczynski and N. Ilten. 18/11/20 ore: 17:00 Soeren Krausshar (University of Erfurt (Germany)) Dipartimento di Matematica, Politecnico di Milano (on line) New results in octonionic monogenic function theory Abstract:In this talk we present a series of new results in octonionic monogenic function theory. We introduce generalizations of the Weierstrass p and zeta function associated with eight-dimensional lattices that have an octonionic multiplication and explain some connections to some possible relations and applications to Class Field Theory. Furthermore, we also give some explicit applications of these kind of functions to the study of Bergman and Hardy spaces in the octonionic cases. Octonionic monogenic generalizations of the cotangent and the cosecant can be obtained as subseries of the octonionic Weierstrass p-functions. These functions turn out to be the building blocks for the reproducing octonionic Bergman and Szegö kernel of strip domains in R^8. Summarizing, these new functions seem to play a key role in octonionic function theories and their applications to number theory and function spaces. 05/11/20 ore: 14:00 Gregory Smith (Queen's University, Kingston, Canada) In remoto - contattare andreas.hochenegger@polimi.it se interessati a partecipare Smooth Hilbert schemes Abstract:How can we understand the closed subschemes in a projective space? Hilbert schemes provide the geometric answer to this question. After surveying some features of these natural parameter spaces, we will classify the smooth Hilbert schemes. Time permitting, we will also describe the geometry of the nonsingular Hilbert schemes by interpreting them as suitable generalizations of partial flag varieties. This talk is based on joint work with Roy Skjelnes (KTH). 22/10/20 ore: 14:00 Emanuele Delucchi (University of Fribourg - Switzerland) Aula seminari terzo piano (link zoom in avviso via mail) On polytopes associated to metric spaces Abstract:Motivated by questions from computational biology, we tackle the problem of a combinatorial classification of finite metric spaces by means of a new polyhedral invariant introduced by Vershik in 2010: the metric space's fundamental polytopes''. These originate from the theory of optimal transport (where they are often named after Wasserstein or Kantorovich-Rubinstein) and have recently found applications in a host of different contexts, from algebraic statistics to tropical geometry to the theory of reaction networks. Nevertheless, the most basic questions on their structure remain to date unanswered. In this talk I will begin by defining the fundamental polytopes of finite metric spaces and sketching the motivation for our work. I will then show how matroid theory allows to describe the combinatorial structure of the fundamental polytopes associated to tree-like metric spaces. I will also discuss some partial results for the case of a special type of phylogenetic networks and, time permitting, I will also present some lines of current research. 21/10/20 ore: 17:00 Pavel Gumenyuk (Politecnico di Milano) On line Loewner's parametric representation in the theory of univalent functions Abstract:The talk is devoted to a rather old topic in Complex Analysis - representation of univalent (= holomorphic and injective) functions of a complex variable via integrals of Loewner's differential equation and its analogues, with applications to problems in conformal mapping. After introducing Loewner's classical method and important results obtained with its help, the main focus will be made on recent developments in the topic for the last 20 years, including applications to univalent functions with quasiconformal extensions and conformal mappings with prescribed boundary fixed points. 04/03/20 ore: 10:45 Gian Maria Dall'Ara (School of Mathematics, University of Birmingham) aula seminari - 3° piano Bergman projections on pseudoconvex domains containing complex manifolds in their boundary 12/09/19 ore: 11:00 Aljosa Volcic (Università della Calabria) Dipartimento di Matematica - 7° piano, Politecnico di Milano Curve di Osgood Abstract:La conferenza sarà dedicata a due argomenti vicini al classico argomento del teorema di Cantor sulla corrispondenza biunivoca (che non può essere continua) tra $[0,1]$ e $[0,1]^2$ ed alla curva di Peano. Principalmente si parlerà di curve create nel 1903 da William F. Osgood il quale costruì, per ogni $\beta \in ]0,1[$ una curva iniettiva la cui immagine ha area $\beta$. Si farà una breve storia di altre costruzioni analoghe, dedicandosi in particolare all'ultima di esse, dovuta a Karl Stromberg e Shiojenn Tseng. In conclusione verrà presentata la dimostrazione dell'esistenza di una curva iniettiva definita su $]0,1[$ la cui immagine ha misura di Lebesgue bidimensionale uguale a $1$. 18/07/19 ore: 10:00 Caterina La Porta (Università degli Studi di Milano) Dipartimento di Matematica - 7° piano, Politecnico di Milano Complexity in biomedicine Abstract:In this talk, I will discuss our recent advances in understanding phenotypic plasticity of cancer cells using a combination of experiments, analysis of big data and computational models of complex regulatory networks. Next, I will discuss our results on protein aggregation in neurodegenerative pathologies, such as Alzheimer's and Huntington's disease. In particular, I will report on the importance of protein clearance from the endoplasmic reticulum to drive protein aggregation and on our recent results on huntingtin heterogenous aggregation in which mutated forms of the protein are able to form oligomers with non-mutated forms. Contacts: paolo.finotelli@polimi.it paolo.dulio@polimi.it 08/07/19 ore: 14:00 Amedeo Altavilla (Università Politecnica delle Marche) Aula Seminari del 3 piano, Edificio La Nave, Via Ponzio 32-34 Implementing zonal harmonics with the Fueter principle Abstract:The Fueter theorem is a well studied result in hypercomplex analysis which gives a procedure to construct hyperholomorphic functions (in some sense), starting from complex holomorphic ones. In this talk I will show how to adapt such result in order to obtain formulas to represent real zonal harmonics in every dimension. 08/07/19 ore: 15:00 Alessandro Monguzzi (Università degli Studi di Milano Bicocca) Aula Seminari del 3 piano, Edificio La Nave, Via Ponzio 32-34 Shift invariant subspaces of the quaternionic space of slice $L^2$ functions Abstract:I will give a characterization of the closed shift invariant subspaces of the quaternionic space of slice $L^2$ functions. As a consequence, the inner-outer factorization theorem for the quaternionic Hardy space $H^2$ on the unit ball is obtained. Therefore, I will present some properties of inner and outer functions in the quaternionic setting, providing in particular sufficient conditions as well as necessary ones for functions to be inner or outer. This talk is based on joint works with Giulia Sarfatti and Daniel Seco. 07/03/19 ore: 14:30 Luca Baracco (Università di Padova) Aula seminari del 3 piano Testing families of analytic discs Abstract: It is a well-known fact in the theory of several complex variables that a function is holomorphic if and only if it is holomorphic in each variable separately. This result goes back to Hartogs. It is natural to consider a boundary version of Hartogs’ theorem. The general problem is to take a boundary function and ask if holomorphic extensions on some families of complex curves are enough to guarantee an extension which is holomorphic in all variables simultaneously. We will talk about the known results on the subject and show some new results obtained in collaboration with M. Fassina and S. Pinton for the spiecial case of the unit ball in C^n. 05/12/18 ore: 11:00 Yuta Kambe (Saitama University) Aula seminari III piano A decomposition of the Hilbert scheme given by Gröbner schemes Abstract:We consider the Hilbert scheme H which is the scheme parameterizing all closed subschemes of the projective space P^n with Hilbert polynomial P. If we fix a monomial order < on the polynomial ring S with n+1 variables, each homogeneous ideal in S has a unique reduced Grobner basis with respect to <. Using this fact we can decompose the Hilbert scheme H into locally closed subschemes of H called the Grobner schemes. On the other hand, Bialynicki-Birula shows that any smooth projective scheme with a 1-dimensional torus action has a cell decomposition called the Bialynicki-Birula decomposition. In this talk, I would like to explain Gröbner schemes and the decomposition. I introduce a 1-dimensional torus action on the Hilbert scheme H which is compatible with < and I show that the decomposition given by the Gröbner schemes can be constructed by such torus action in the sense of Bialynicki-Birula. 05/12/18 ore: 12:00 Alessandro Oneto (Barcelona Graduate School of Mathematics) Aula seminari III piano Waring loci and decompositions of low rank symmetric tensors Abstract:Given a symmetric tensor, i.e., a homogeneous polynomial, a Waring decomposition is an expression as sum of symmetric decomposable tensors, i.e., powers of linear forms. We call Waring rank of a homogenous polynomial the smallest length of such a Waring decomposition. Apolarity theory provides a very powerful algebraic tool to study Waring decompositions of a homogeneous polynomial by studying sets of points apolar to the polynomial, i.e., sets of points whose defining ideal is contained in the so-called apolar ideal of the polynomial. In this talk, I want to introduce the concept of Waring locus of a homogeneous polynomial, i.e., the locus of linear forms which may appear in a minimal Waring decomposition. Then, after showing some example on how Waring loci can be computed in specific cases via apolarity theory. I explain how they may be used to construct minimal Waring decompositions. These results are from recent joint works with E. Carlini, M.V. Catalisano, and B. Mourrain. 11/09/18 ore: 14:15 Andrzej Kisielewicz (Uniwersytet Wroc?awski, Wydzia? Matematyki i Informatyki) Aula seminari III piano KöNIG'S PROBLEM FOR ABELIAN PERMUTATION GROUPS Abstract:König's problem for permutation groups concerns the following question: Given a permutation group P = (P, X) acting on a finite set X, is there a graph G=(G, X) with the set of vertices X, such its automorphisms are precisely permutations in P? König's problem is to find a necessary and sufficient conditions for a permutation group P to be the automorphism groups of some graph. There exist permutation groups that are not the automorphism groups of any graph (for example, alternating groups or groups generated by a single cyclic permutation). So far, this version of König’s problem (known also as the concrete version) has been solved only for regular permutation groups, cyclic permutation groups (generated by a single permutation), and partially, for abelian permutation groups. In this talk we demonstrate however that the result by Zelikovskij [3] concerning König's problem for abelian permutation groups, reported in a recent survey [2], is false. We argue that a more natural setting for this problem is that concerning the automorphism groups of edge-colored graphs. Our main result, based on techniques applied in [1], provides a characterization of those abelian permutation groups that are the automorphism groups of edge-colored graphs and shows, in addition, that each such group can be represented by an edge-colored graph using no more than 4 colors. References [1] M. Grech, A. Kisielewicz, Symmetry groups of boolean functions, European J. Combin. 40 (2014) 1-10. [2] J. Morris, Automorphism Groups of Circulant Graphs - a Survey, in: Bondy A., Fonlupt J., Fouquet JL., Fournier JC., Ramrez Alfonsn J.L. (eds) Graph Theory in Paris. Trends in Mathematics. Birkhuser Basel 2006, pp. 311-325. [3] A. Z. Zelikovskij, Konigs problem for Abelian permutation groups, Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk 5 (1989), 34-39. 19/06/18 ore: 14:30 Emanuele Macrì (Northeastern University, Department of Mathematics) Aula seminari del terzo piano Bridgeland stability and the genus of space curves Abstract:I will give an introduction to various notions of stability in the bounded derived category of coherent sheaves on the three-dimensional projective space. As application I will show how to possibly use these techniques towards the study of space curves. This is joint work with Benjamin Schmidt. 08/06/18 ore: 14:30 Joachim Jelisiejew (Institute of Mathematics, Polish Academy of Sciences) Aula seminari del terzo piano Bialynicki-Birula decompositions and the Hilbert scheme of points Abstract:In the talk I will briefly describe how a group action can be used to analyse a moduli space (or more generally, a functor) via a generalization of the Bialynicki-Birula decomposition. As a half-of-the-talk-example I will explain what can be said for the Hilbert scheme of points on A^n (n>2) and in particular how to exhibit its components. In the last part I'll carefully review open questions: on the one hand, the newly exhibited smooth components are open to direct or experimental investigation and on the other hand, the new methods may help to answer classical open questions about those Hilbert schemes. 31/05/18 ore: 14:30 Cinzia Bisi (Università di Ferrara) Aula Seminari III piano On the harmonicity of slice regular functions Abstract: I will start improving the definition of slice regular function over the quaternions given by Gentili-Struppa in 2006-2007. Then, bringing new ideas to the theory, I will answer positively to the question: is a slice regular function over the quaternions (analogously to a holomorphic function over the complex) ”harmonic” in some sense, i.e. is it in the kernel of some order-two differential operator over the quaternions? Finally, I will deduce novel integral formulas as applications. This is part of a common project with J. Winkelmann. 12/04/18 ore: 14:30 Michele Rossi (Università di Torino) Aula seminari del terzo piano Non-canonical embeddings and a canonical torsion-free covering for Mori Dream Spaces Abstract:The talk will be divided in two parts, approximately 45 minutes each; the first part is intended to be an introduction to the more technical second part; there will be a brief break between the two parts. In the first part of this talk I will recall a standard construction of an (almost)-canonical toric embedding of a (non-necessarily projective) Mori Dream Space (MDS), starting from its Cox ring. Moreover I will recall some notation about the GKZ-decomposition of the pseudo-effective and the moving cone of a MDS. In the second part we will see some obstruction to extending Hu-Keel birational geometric results to the non-projective setup. Then I will show how recent results, jointly obtained with L. Terracini for $\Q$-factorial complete toric varieties, can be easily extended to a general MDS, producing a projective embedding of every MDS of Picard number less than or equal to 2 and a canonical covering space, unramified in codimension 1, of a given MDS, which is still a MDS admitting a torsion-free class group. In principle, an application of such a covering construction is that the Cox ring of a MDS, which is in general graded over a class group with non trivial torsion part, could be described in terms of the Cox ring of its canonical covering, which is now graded over a torsion-free class group. This is a work in progress. 15/03/18 ore: 14:00 Chiara de Fabritiis (Università Politecnica delle Marche) Aula seminari del terzo piano One-Slice Preserving Functions of a Quaternionic Variable Abstract:Regular functions on the skew-field of quaternions were introduced by Gentili and Struppa some 10 years ago in order to give an analogue of holomorphic functions in a non commutative setting. After a (short) introduction, I will give a formula which allows us to simplify the understanding of the *-product, which corresponds to the pointwise product of holomorphic functions. The peculiar structure of quaternions, foliated in copies of complex plane, drives naturally to consider the classes of functions which preserve either one or all complex slices. The main part of the talk will be devoted to characterize the functions whose sum, *-product or conjugate preserve a slice. At the end, time permitting, I will address to the case of *-powers which shows an unexpected connection with a problem of algebraic geometry studied by Causa and Re. (Joint work with A. Altavilla) 08/03/18 ore: 14:30 Delaram Kahrobaei (New York City College of Technology) Aula seminari, III piano, Dipartimento di matematica Post-Quantum Group-based Cryptography Abstract:The National Security Agency (NSA) in August 2015 announced plans to transition to post-quantum algorithms “Currently, Suite B cryptographic algorithms are specified by the National Institute of Standards and Technology (NIST) and are used by NSA’s Information Assurance Directorate in solutions approved for protecting classified and unclassified National Security Systems (NSS). Below, we announce preliminary plans for transitioning to quantum resistant algorithms.” Shortly after the National Institute of Standardization and Technology (NIST) announced a call to select standards for post-quantum public-key cryptosystems. The academic and industrial communities have suggested as the quantum-resistant primitives: Lattice-based, Multivariate, Code-based, Hash-based, Isogeny-based and group-based primitives. In this talk I will focus on some ideas of (semi)group-based primitives. The one which was proposed to NIST is by SecureRF company based in Connecticut, among its founders there is a number theorist (Goldfeld) and two group theorists (Anshel and Anshel). They proposed a digital signature using a hard algorithmic problem in Braid groups, namely conjugacy problem. I will then give a survey of some other suggested group-based cryptosystems that could be claimed as post-quantum cryptosystems. 26/01/18 ore: 15:30 Filippo Viviani (Universita' Roma Tre) Aula seminari del terzo piano On the cone of effective cycles on the symmetric products of a curve Abstract:I will report on a joint work with F. Bastianelli, A. Kouvidakis and A. F. Lopez in which we study the cone of (pseudo-)effective cycles on symmetric products of a curve. We first prove that the diagonal cycles span a face of the pseudo-effective cone of cycles in any given dimension. Secondly, we look at the contractibility faces associated to the Abel-Jacobi morphism towards the Jacobian and in many cases we are able to compute their dimension. The geometry of linear series of a curve (e.g. the classical Brill-Noether theory) will play a special role in our analysis. 12/01/18 ore: 15:30 Marta Panizzut (TU Berlin) Aula seminari del terzo piano TROPICAL APPROACHES TO BRILL–NOETHER THEORY Abstract:Loosely speaking, tropical geometry aims to transform algebro-geometric problems into combinatorial ones that are hopefully easier to understand. Tropical curves are connected metric graphs, and a theory of linear systems on graphs has been introduced by Baker and Norine in analogy with the one on algebraic curves. Their groundbreaking work has led to the development of a tropical Brill–Noether theory, which provides new combinatorial insights in the study of linear systems on curves. The interplay between the tropical and the classical theory is given by specialization of linear systems from the generic fiber of a 1-parameter family of curves to the dual graph of the special fiber. In this talk, I will begin by introducing the terminology and some of the main results of this recent theory. Then I will address questions on smooth plane curves and generic smooth curves on P1 × P1 by specializing their linear systems to complete graphs and complete bipartite graphs. This based on joint works with with Filip Cools, Michele D’Adderio and David Jensen. 16/06/17 ore: 14:15 Junling Zhou (Department of Mathematics, Beijing Jiaotong University, P. R. China) Aula seminari III piano Large sets of Kirkman triple systems Abstract:Research on the existence of large sets of Kirkman triple systems (LKTS) extends from the mid-eighteen hundreds to the present. However this problem is still wide open until now. In this talk, direct and recursive constructions of LKTS will be reviewed. Some new results will be introduced. 16/06/17 ore: 14:40 Tao Feng (Department of Mathematics, Beijing Jiaotong University, P. R. China) Aula seminari III piano Decompositions of the complete n-partite equipartite multigraph with any minimum leave and minimum excess Abstract:A decomposition of ?K_n(g) \ L, the complete n-partite equipartite multigraph with a subgraph L (called the leave) removed, into edge disjoint copies of a graph G is called a maximum group divisible packing of ?K_n(g) with G if L contains as few edges as possible. A decomposition of ?K_n(g) ? E, the complete n-partite equipartite multigraph union a graph E (called the excess), into edge disjoint copies of a graph G is called a minimum group divisible covering of ?Kn(g) with G if E contains as few edges as possible. We continue Billington and Lindner’s work in [1] to examine all possible minimum leaves for maximum group divisible packings of ?Kn(g) with G and all possible excesses for minimum group divisible coverings of ?Kn(g) with G, where G is a triangle K3, or a triangle plus one dangling edge K3 + e, or K4 ? e [2, 3]. When G is K4, the problem is closely related with many other combinatorial con?gurations, such as balanced sampling plans excluding contiguous units, matching divisible designs, etc. We shall show that the obvious divisibility conditions are su?cient for the existence of matching divisible designs with block size four [4]. References [1] E.J. Billington, C.C. Lindner, Maximum packings of uniform group divisible triple systems, J. Combin. Designs, 4 (1996), 397–404. [2] X. Hu, Y. Chang, and T. Feng, Group divisible packings and coverings with any minimum leave and minimum excess, Graphs and Combinatorics, 32 (2016), 1423–1446. [3] Y. Gao, Y. Chang, and T. Feng, Group divisible (K4 ? e)-packings with any minimum leave, arXiv:1705.08787. [4] P.J. Dukes, T. Feng, A.C.H. Ling, Matching divisible designs with block size four, Discrete Math., 339 (2016), 790–799. 16/06/17 ore: 15:30 Yanxun Chang (Department of Mathematics, Beijing Jiaotong University, P. R. China) Aula seminari III piano Designs with speci?c automorphism group Abstract:Let v, k and t be positive integers such that v > k > t. A Steiner t-wise balanced design (brie?y S(t,k,v)) is a pair (X,B), where X is a set of v points and B is a set of k-subsets of X (called blocks) such that every t-subset of X is contained in a unique block. An automorphism group of a S(t,k,v) (X,B) is a permutation group on X leaving B invariant. In this talk, we consider Steiner t-wise balanced design with speci?c automorphism. Some direct and recursive constructions on this topics are summarized. 30/05/17 ore: 14:30 Dott.ssa Eulàlia Tramuns Figueras ( ) aula F. Saleri - 6° piano - edificio 14 - Nave On the axiomatization of origami and other geometric instruments 30/05/17 ore: 15:15 Dott.ssa M.L. Sonia Spreafico ( ) aula F. Saleri - 6° piano - edificio 14 - Nave Didattica con l'origami in università 28/04/17 ore: 14:00 Paula Cerejeiras (Università di Aveiro) Aula Seminari del 3 piano Reproducing Kernel Hilbert Spaces in the context of Fractional Derivatives Abstract:The idea of a fractional calculus - as already suggested by Leibniz - has seen an increasing interest due to the possibilities for a more accurate description of numerous physical problems either because it provides a new degree of freedom which can be used for more complete characterization of an object or as an additional encoding parameter. In this talk we present a general framework for a function theory based on fractional Cauchy-Riemann operators. Using suitable basic monogenic powers and associated Fueter series we study Gleason's problem and reproducing kernel Hilbert spaces, like the Drury-Arveson space and de Branges-Rovnyak space. We present a counterpart of the Beurling-Lax theorem in the fractional Clifford-Arveson space and give a characterization of the Schur-Agler classes. If time allows we will end with a statement on Schur multipliers in this fractional setting. 17/02/17 ore: 14:00 Paolo Stellari (Università di Milano) Aula Seminari del terzo piano A derived category approach to some moduli spaces on cubic threefolds and fourfolds. Abstract:We exploit the homological properties and the geometric meaning of Kuznetsov's semiorthogonal decomposition of the derived categories of cubic fourfolds (and threefolds) to study the (birational) geometry of some interesting moduli spaces on such varieties. We will start working out the very instructive example of the moduli space of stable aCM bundles of a given rank on a cubic threefold. Then we will discuss our main result concerning the case of generalized twisted cubics on cubic fourfolds not containing a plane. We will show that we can recover the picture by Lehn-Lehn-Sorger-van Straten in terms of moduli spaces of (weakly) stable sheaves/complexes. This is joint work with M. Lahoz, M. Lehn, and E. Macri'. 20/12/16 ore: 15:00 Tommaso Traetta (Department of Mathematics, Ryerson University) Aula Seminari Terzo Piano Open problems on 2-factorizations and new powerful methods to attack them Abstract:A 2-factorization of a graph G is a set F of spanning 2-regular subgraphs (i.e., 2-factors) whose edge-sets partition the edge-set of G. It is well known that G has a 2-factorization if and only if it is regular of even degree. However, if we specify t 2-factors, say F1, F2, ..., Ft, and ask for the factorization F to contain ?_i factors isomorphic to Fi, then the problem becomes much harder. When t = 1 we have the well-known Oberwolfach problem, attributed to G. Ringel who posed it in 1956. The case t = 2 is known as the Hamilton-Waterloo problem, whereas for greater values of t we speak of the generalized Oberwolfach problem. The case where t ? {1, 2} and G is the complete (equipartite) graph is the most studied one. Nonetheless, these problems are still open although they have received much attention lately. In this talk I will emphasize the connection between 2-factorizations and sharply transitive sets of permutations. Then, I will focus on some of the most recent results and their powerful algebraic methods. This seminar is organized within the PRIN 2012 Research project «Geometric Structures, Combinatorics and their Applications» Grant Registration number 2012XZE22K, funded by MIUR - Project coordinator Prof.ssa Norma Zagaglia 12/12/16 ore: 14:30 Natasha Jonoska (University of South Florida) Aula seminari III piano Using spacial graphs to study reoccurring patterns of scrambled genes Abstract:Nucleotide rearrangements occur at both evolutionary and developmental levels, and are often studied through model organisms such as ciliate species Oxytricha and Stylonychia. These processes can be modeled by 4-regular rigid vertex graphs, called assembly graphs. They are closely related to double occurrence words, chord diagrams, and circle graphs. Edges of these graphs represent double-stranded DNA molecules, while vertices correspond to DNA recombination sites. We present graph invariants of these assembly graphs and investigate genome-wide the range of scrambled gene architectures that describe the precursor-product relationships. We find that there are two general patterns, reoccurring genome wide, that describe over 90% of the Oxytricha’s scrambled genes. We further investigate the patterns of interleaving genes and find that there are specific star-like graph structures that describe most complex interleaving patterns. 21/10/16 ore: 14:00 Stefano Urbinati (Università di Padova) Aula Seminari del terzo piano Tropical compactifications, Mori Dream Spaces and Minkowski bases Abstract:Given a Mori Dream Space X we construct via tropicalization a model dominating all the small Q-factorial modifications. Via this construction we recover a Minkowski bases for the Newton-Okounkov bodies on X and hence the movable cone for X. This is a work in progress with Elisa Postinghel. Nota dell'organizzatore (E. Schlesinger): Stefano Urbinati ha vinto una Polimi International Fellowship e prenderà presto servizio presso il nostro dipartimento; lavora nell'ambito della geometria algebrica e ultimamente si è interessato a problemi di geometria tropicale. 27/09/16 ore: 11:00 Emanuele Brugnoli (Università di Palermo) Aula seminari III piano Graph decompositions via integer compositions Abstract:A composition of a positive integer n is defined as a way of writing n as an ordered sum of positive integers (parts). The study of compositions has a long and rich history. The earliest publication on this subject is by Percy Alexander MacMahon in 1893, entitled Memoir on the Theory of Compositions of a Number and started with the words Compositions are merely partitions in which the order of occurrence of the parts is essential.'' MacMahon derived a number of results, for example the total number of compositions and the number of compositions with a given number of parts, using generating functions. Since the second half of 20th century, several groups of authors developed new research directions studying compositions restricted in some way, as also certain characteristics of these compositions. In this talk, the strict connection between integer compositions and graph decompositions into Hamiltonian cycles is shown. Denoting, as usual, with K_v the complete graph on v vertices, a Hamiltonian cycle system of odd order v (briefly HCS(v)) is a set of Hamiltonian cycles of K_v whose edges partition the edge-set of K_v. The earliest example of a HCS(2n+1) is attributed to Walecki; its vertex-set is V_{2n+1} := Z_{2n} U { ? } and it consists of all cycles belonging to the orbit of the starter cycle ( ?, 0, 1, -1, 2, -2, …, i, -i, …, n-1, -(n-1), n ) under the natural action of Z_{2n} on V_{2n+1}. By means of a slight modification of the HCS(4n+1) of Walecki, we obtain 2^n pairwise distinct HCS(4n+1) and we enumerate them up to isomorphism proving that this result can be achieved by counting the inequivalent compositions of n under the action of D_n, the dihedral group of order 2n. This seminar is organized within the PRIN 2012 Research project «Geometric Structures, Combinatorics and their Applications» Grant Registration number 2012XZE22K, funded by MIUR - Project coordinator Prof.ssa Norma Zagaglia 10/06/16 ore: 10:00 Christian Choffrut (Université de Paris-Diderot - Paris 7) Aula seminari-III piano Un sotto-monoide degli endomorfismi invertibili del monoide libero. Abstract:Motivati dalla sfida di descrivere tutte le soluzioni di una equazione nel monoide libero, abbiamo studiato il sottomonoide proprio N del monoide di tutti gli endomorfismi invertibili del monoide libero generati dai morfismi f del seguente tipo: siano a, b due lettere arbitrarie del monoide libero,f mappa a su ba e lascia tutte le altre lettere invarianti, per esempio: f(cabba) = cbabbba. Dirò rapidamente come questa problematica si inserisce nella teoria delle equazioni del monoide libero. Ricorderò i risultati anteriori delle letteratura. Presentrò i nostri risultati: una presentazione (“monoid presentation”) di N, una procedura che risolve il problema dell’appartenanza di un morfismo ad N e la soluzione del problema della parola (“word problem”) in N. 26/05/16 ore: 14:00 Riccardo Re (Università di Catania) Aula Seminari del terzo piano Normal bundles of rational curves and applications Abstract:We introduce a new technique to effectively compute the normal bundle of a parametrized rational curve in a projective space. As an application we show how to construct counterexamples to the question, dating from the '80s, whether the Hilbert space of rational curves with a given splitting type of the normal bundle is irreducible. If time permits, we will apply our results to monomial curves and give a formula for their Castelnuovo-Mumford regularity. 25/05/16 ore: 14:00 Daniele D'Angeli (Institute fur Diskrete Mathematik TU Graz) Aula seminari III piano An invitation to automata groups Abstract:The purpose of this talk is to give a very gentle introduction to the theory of automaton groups and related topics. An automaton group is defined by the action of a Mealy machine on the set of words over a finite alphabet, or by the action via automorphisms on a rooted tree. This class of groups contains groups with exotic and special properties and it has been used to solve open problems or disprove conjectures in several areas of Mathematics. I will present some interesting examples of automaton groups, and their connections with different areas of Mathematics such as Graph Theory, Complex Dynamics and Computer Science. 20/05/16 ore: 14:30 Anna Miriam Benini (Universita' di Roma Tor Vergata) Aula seminari del terzo piano Repelling periodic points for transcendental entire functions Abstract:How many repelling periodic points of any period does a transcendental function have? For a generic rational function, the number of periodic points can be easily counted using the degree, and by the Fatou Shishikura inequality all but finitely many are repelling. Entire functions in general do not even need to have fixed points,see for example e^z+z. However we will be able to show-with a rather elementary proof- that for several important classes of transcendental functions there are-as expected-infinitely many repelling periodic points of any given period,and give some more information on the way they are distributed in the dynamical plane. 11/05/16 ore: 14:30 Hendrik De Bie (Ghent University) Aula seminari del 3 piano Uni- and multivariate discrete orthogonal polynomials using Dirac operators Abstract:In the second talk, we will reverse the question of the previous talk. Given a family of discrete orthogonal polynomials, can we construct a Dirac model so that they arise as expansion coefficients? We will answer this question affirmatively for the Racah polynomials and their generalization the Bannai-Ito polynomials. In the univariate case we will use a generalized Dirac operator in 3D, while for the multivariate case we have to resort to nD. Along the way, we will construct a new symmetry algebra that can be interpreted as a higher rank Bannai-Ito algebra. 09/05/16 ore: 10:30 Hendrik De Bie (Ghent University) Aula seminari del 3 piano Spherical monogenics in dimension 3 and discrete orthogonal polynomials Abstract:In this educational talk, my main goal is to show how a family of discrete orthogonal polynomials from the Askey scheme naturally arises in the study of spherical monogenics in dimension 3. This connection will be revealed by making explicit the action of the so(3) Lie algebra that preserves the monogenics on a basis constructed using a tower of CK extensions. It will then be shown that different towers of CK extensions lead to different orthogonal bases. The expansion coefficients between two such bases are subsequently expressed using the Krawtchouk discrete orthogonal polynomials. 02/05/16 ore: 11:30 Nicola Arcozzi (Università di Bologna) Aula seminari del terzo piano The Dirichlet Space on the bi-disc Abstract:The analytic Dirichlet space on the complex disc is rather well understood and its counterpart on the unit ball in several complex dimensions shares with it many important features. For instance, there is a natural underlying (sub-Riemannian) geometry, with the obvious one-parameter family of metric balls having center at a given point. Things become drastically different in the bidisc, where genuine two-parameter phenomena appear. I will review what is known about this holomorphic space, including recent results in collaboration with Pavel Mozolyako, Karl-Mikael Perfekt, Giulia Sarfatti. 21/04/16 ore: 14:30 Paolo Finotelli (Politecnico di Milano) Aula Seminari del terzo piano del Dipartimento di Matematica del Politecnico di Milano (via Bonardi 9, MIlano, Edificio 14 “La Nave”) EXPLORING FUNCTIONAL CONNECTIVITY USING A NOVEL GRAPH MODEL: PRESENT APPLICATIONS AND FUTURE PERSPECTIVES Abstract:In this talk we wish to present a new mathematical model for evaluating the functional connectivity in brain networks. A brief introduction on the basic neuroscientific and mathematical tools will be provided. Then the parameters involved in the model will be detailed and discussed, together with some applications and possible perspectives. 08/04/16 ore: 14:30 Samuele Mongodi (Università di Pisa) Aula seminari del terzo piano Misure di Carleson e operatori di Toeplitz in domini strettamente pseudoconvessi limitati Abstract:Le misure di Carleson furono introdotte da Carleson per studiare il problema della corona; una misura $\mu$ è di Carleson per uno spazio di Banach $A$ di funzioni olomorfe se A si immerge con continuità in $L^p(\mu)$. Una delle prime domande che ci si pone è come caratterizzare le misure di Carleson tramite proprietà geometriche del dominio, preferibilmente invarianti per biolomorfismo. Per un generico limitato strettamente pseudoconvesso, questo è stato fatto da Abate, Raissy e Saracco, stabilendo un legame tra le misure di Carleson, la trasformata di Berezin e gli operatori di Toeplitz, entrambi questi ultimi definiti in termini del nucleo di Bergman del dominio. In questo seminario, presenterò questi risultati e parlerò di alcune generalizzazioni che sto studiando attualmente. 25/02/16 ore: 15:30 Guglielmo Albanese (Università degli Studi di Milano) Aula seminari del 6 piano, Edificio La Nave, Dipartimento di Matematica, Via Bonardi 9, Milano SEMILINEAR ELLIPTIC PDES ON COMPLETE MANIFOLDS WITH BOUNDARY Abstract:(Il seminario del 18 febbraio è cancellato per indisposizione del relatore) 19/02/16 ore: 15:30 Barbara Fantechi (Sissa) Aula seminari terzo piano (Dipartimento di matematica) Local triviality of infinitesimal deformations for varieties with quotient singularities Abstract:Let V be a complex projective variety with at most quotient singularities. If V is smooth, all infinitesimal deformations are locally trivial; Schlessinger proved in 1968 that the same is true if the singularities are in codimension greater or equal to 3. Let (S,p) be an (\'etale or formal) germ of a (necessarily isolated) surface quotient singularity; we say that V has transversal singularities of type (S,p) along a locally closed smooth subvariety Y if \'etale locally the pair (V,Y) is isomorphic to (S,p) times Y. In case all codimension 2 singularities of V are transversal of type A_{n-1} (that is 1/n(1,n-1)) or 1/n(1,1), we give sufficient conditions to guarantee that all infinitesimal deformations are locally trivial. As an application, we show that \bar M_{g,n}, the variety of n-pointed stable curves of genus g, is rigid (i.e., has no nontrivial infinitesimal deformations) for all but a finite number of values for (g,n). This is partially joint work with Alex Massarenti. 12/01/16 ore: 11:00 Vincenzo Recupero (Politecnico di Torino) Aula seminari del 6 piano, Dipartimento di Matematica, Via Bonardi 9, Milano Analytic semigroups in the noncommutative framework Abstract:Functional analysis in Banach spaces over the skew field H of quaternions is receiving increasing attention and relies upon the theory of slice regular functions, the quaternionic counterpart of analytic functions. In this talk we introduce the class of sectorial operators on these spaces and we prove that they generate a one quaternionic parameter operator family which is slice regular and satisfies a new semigroup law induced by the noncommutative structure of H. Moreover these semigroups can be represented by a suitable Cauchy integral formula. These results can be generalized to spaces over any finite dimensional real involutive algebra, Clifford algebras included. 23/11/15 ore: 14:30 Paula Cerejeiras, Uwe Kaehler (University of Aveiro) Aula seminari del 3 piano Course: Clifford analysis techniques in image processing Abstract:The course is intended to give an overview of applications of Clifford analytic methods to problems in signal and image processing. Since the principal fields of application are currently in the area of encoding of color image and edge detection we shall present examples of Clifford analytic methods for these problems. In the case of color imaging we will discuss the problem of sparse representation and applications of compressed sensing methods. For edge detection we introduce the monogenic signal and construct appropriate frames for it. Two principal examples of such frames will be given: Monogenic wavelets and monogenic curvelets. Since Clifford analysis techniques are strongly linked with geometric aspects of the underlying space we will show the limits of these approaches by discussing the problem of constructing monogenic shearlets. If there is time we intend to discuss also the natural question of the corresponding coorbit space theory. In any case we are going to show the practical problems arising in the implementation of these methods and give some examples in Matlab. The schedule of the course is availaible at the link https://www.mate.polimi.it/upload/Clifford%20analysis%20techniques%20in%20image%20processing.pdf 01/10/15 ore: 11:15 Disanto Filippo (Stanford University, CA) Aula seminari III piano ASPETTI COMBINATORI DELLA INFERENZA DI ALBERI DI SPECIE DA ALBERI DI GENI Abstract:Alberi di specie, rappresentanti le dinamiche evolutive tra specie, possono esseri stimati con metodi statistici a partire da collezioni di alberi di geni che rappresentano l'evoluzione di singoli individui appartenenti alle specie considerate. Tale problema di inferenza statistica presenta nelle sue componenti di accuratezza e complessità computazionale diversi aspetti combinatori. In questo ambito, le tematiche oggetto della presentazione saranno le seguenti due: a) Risultati recenti sulla esistenza e probabilità, nel modello stocastico di coalescenza multispecie, di alberi di geni "anomali". Fissata una topologia per l'albero di specie, questa si dice produrre un albero di geni anomalo quando esiste un insieme di lunghezze (cioè tempi evolutivi) per i suoi rami per cui l'albero di geni più probabile nel modello stocastico ha una topologia diversa da quella dell'albero di specie. L'esistenza di alberi di geni anomali pone limiti all'uso di metodi statistici di consenso per la stima degli alberi di specie a partire dall'analisi delle sequenze genetiche di singoli individui. b) La complessità in tempo di alcuni metodi di inferenza degli alberi di specie dipende dalla velocità con cui si riesce a calcolare la probabilità condizionata, Prob(G|S), di una topologia di albero di geni G per una fissata topologia di albero di specie S. Il tempo necessario per calcolare Prob(G|S) dipende intrinsecamente, a sua volta, dal numero di possibili configurazioni, h(G,S), che l'albero G può assumere nella struttura di S. Tali configurazioni, h(G,S), vengono dette "storie di coalescenza" di G in S e la loro enumerazione è oggetto di interesse. Si presenteranno recenti risultati enumerativi sul calcolo della cardinalità di h(G,S) assumendo che gli alberi G ed S abbiano la stessa topologia e che questa appartenga a particolari famiglie di alberi non bilanciati. Questo seminario è organizzato nell'ambito del PRIN 2012, progetto di ricerca «Strutture Geometriche, Combinatoria e loro Applicazioni» Protocollo n° 2012XZE22K_004, cofinanziato dal MIUR – Responsabile Scientifico dell'Unità di ricerca: Prof.ssa Norma Zagaglia 08/07/15 ore: 14:30 Alberto Saracco (Università di Parma) Aula Seminari del terzo piano Carleson measures in strongly pseudoconvex domains Abstract:Since 1962 Carleson measures were introduced to solve the corona problem, they have been both an important tool and an interesting mathematical object to study per se. In this talk I will review some important characterizations of Carleson measures for Hardy or Bergman spaces of function in the unit disc or the unit ball, due to several authors. Then I will expose our recent intrinsic characterization of Carleson measures for Bergman spaces in strongly pseudoconvex domains of C^n and related results. (joint works with Marco Abate and Jasmin Raissy) 19/06/15 ore: 15:00 Robin Hartshorne (U.C. Berkeley ) Aula Seminari Mox del sesto piano D-modules and local cohomology Abstract:The concept of modules over a ring with differential operators is an old one, but its relevance to commutative algebra dates from 1993, when Lyubeznik discovered that the local cohomology module of a polynomial ring with supports in any ideal is a finitely generated D-module, even though it is rarely finitely generated over the polynomial ring. In fact these modules are what is called holonomic, i.e. of finite length over the ring of differential operators. I will explain the ideas behind this discovery, and tell how it has helped to prove new finiteness theorems about these mysterious modules. 05/05/15 ore: 11:30 Tim Janssens (University of Antwerp (Belgium)) Aula Seminari del terzo piano Special functions in higher spin Clifford analysis 24/04/15 ore: 11:30 Amedeo Altavilla (Università di Trento) Aula Seminari del terzo piano On the singular set of a slice regular function Abstract:In this talk I will present some results in the analysis of the real differential of a slice regular function. I will describe the set of singular points of a slice regular function and I will prove a couple of results regarding the behavior of its partial derivatives. This talk is mainly based on a work available at http://arxiv.org/abs/1402.3993. 18/09/14 ore: 14:30 Daniel Alpay (Ben Gurion University, Beer Sheva) Aula Seminari del 3 piano Dip. Matematica (Ed. 14) Reproducing kernel Hilbert spaces, linear (deterministic and stochastic) systems and inverse scattering Abstract:Functions analytic and contractive in the open unit disk play a key role in a host of mathematical domains, for instance operator models, inverse scattering and linear systems. We first discuss the main points in this circle of ideas. The reproducing kernel Hilbert spaces of the kind introduced by de Branges and Rovnyak are an important tool in the arguments. In the second part of the talk we study the stochastic analogs of the situation above. The complex numbers are then replaced by an algebra of stochastic distributions, with a very special structure. it is the dual of a nuclear Fréchet space, and a countable union of increasing Hilbert spaces with decreasing norms, the norms being related by a family of inequalities. Finally we briefly outline the free analog of these spaces of stochastic distributions. References: D. Alpay. The Schur algorithm, reproducing kernel spaces and system theory, volume 5, SMF/AMS Texts and Monographs of the Société mathématique de France (2001). D. Alpay and I. Gohberg. Discrete systems and their characteristic spectral functions. Mediterrean Journal of Mathematics, vol. 4 (2007), pp. 1-32. D. Alpay, P. Jorgensen and D. Levanony. A class of Gaussian processes with fractional spectral measures. Journal of Functional Analysis, Volume 261 (2011), pp. 507-541. D. Alpay and G. Salomon. Non-commutative stochastic distributions and applications to linear systems theory. Stochastic Processes and their Applications, vol. 123 (2013), pp. 2303-2322. D. Alpay, P. Jorgensen and G. Salomon: On free stochastic processes and their derivatives. Stochastic Processes and their Applications, vol. 214 (2014), 3392-3411. 16/09/14 ore: 14:00 Akhtam Dzhalilov (Turin Polytechnic University in Tashkent, Uzbekistan) Aula seminari del 3 piano Invariant measures, conjugacies and renormalizations of piecewise-smooth circle maps Abstract:The class of orientation preserving circle homeomorphisms is one of important part of one-dimensional dynamical systems. We will consider piecewise-smooth circle homeomorphisms f with finite many break points, that is, maps that are smooth everywhere except for several singular points at which the first derivative Df has a jump. It is well known that the invariant measures of sufficiently smooth circle diffeomorphisms are absolutely continuous w.r.t. Lebesque measure. But in the case maps with break points the results are quite different. We formulate the main results on invariant measures, conjugacies and renormalizations of piecewise-smooth diffeomorphisms with finite many break points. 08/05/14 ore: 11:30 Paolo Lella (Dipartimento di Matematica, Università di Torino) Aula seminari III piano Il grado di massima verosimiglianza delle ipersuperfici di Fermat Abstract:Uno degli strumenti classici per affrontare problemi di ottimizzazione statistica è il metodo di massima verosimiglianza. Nel caso di modelli statistici algebrici, cioè di modelli nei quali le relazioni tra le variabili aleatorie sono polinomiali, applicare questo metodo significa studiare i punti critici della funzione di massima verosimiglianza che appartengono al luogo di annullamento dei polinomi. Il numero di punti critici risulta essere un invariante topologico della varietà e viene detto grado di massima verosimiglianza. Nel seminario studierò il grado di massima verosimiglianza delle ipersuperfici di Fermat. Le ipersuperfici di Fermat non hanno un chiaro significato statistico, ma il loro studio rappresenta un significativo esempio delle potenzialità dell applicazione di strumenti tipici della geometria algebrica al campo della statistica algebrica. Si tratta di risultati ottenuti in collaborazione con D. Agostini, D. Alberelli e F. Grande. 19/03/14 ore: 15:15 Giovanni Manno (Università di Padova) Aula Seminari, III piano Geometria di contatto delle PDEs Abstract:Vedremo come la geometria di contatto/simplettica giochi un ruolo fondamentale nella classificazione delle PDEs del second ordine. Tratteremo quindi, in maggior dettaglio, il caso delle equazioni di Monge-Ampère, che geometricamente si possono interpretare come distribuzioni vettoriali su una varietà di contatto. Discuteremo infine un problema formulato originariamente da Sophus Lie (1874), tuttora aperto. 13/02/14 ore: 00:00 Rogério Reis (Centro de Matemática da Universidade do Porto) Aula PT1-DEIB Measuring average complexity of automata operations Abstract: The worst-case complexity of the conversions between different representations of regular languages is well studied. However, for practical purposes, the average-case complexity of such conversions is much more relevant than its worst-case complexity, which is often due to some particular and rarely occurring cases. Still, the average-case analysis is, in general, a difficult task. One approach is to consider uniform random generators and to perform statistically significant experiments. Another approach is the use of asymptotic methods. In this presentation, we discuss asymptotic average-case results on the size of non-deterministic finite automata obtained from regular expressions, using the symbolic method and the framework of analytic combinatorics. 19/09/13 ore: 11:00 Paolo Dulio (Dipartimento di Matematica) Dipartimento di Matematica, Aula Seminari terzo piano Explicit Determination of Bounded Non-Additive Sets of Uniqueness for Four X-rays Abstract:An algorithm is presented which constructs bounded non-additive sets uniquely determined by discrete parallel X-rays taken along prescribed lattice directions. Examples in dimension n=2 and n=3 are given, and related remarks are also provided 09/05/13 ore: 14:30 Adriano Tomassini (Università di Parma) Aula Seminari del 3 piano Scomposizioni coomologiche di varietà complesse Abstract:Recentemente alcuni autori hanno studiato le proprieta coomologiche delle varietà quasi complesse e complesse. In questo seminario, saranno esaminate varie scomposizioni coomologiche su varieta complesse non kahleriane. In particolare, sarà data una caratterizzazione in termini dei gruppi di coomologia di Bott-Chern delle varietà complesse compatte che verificano il $partial bar partial$-Lemma. 28/11/12 ore: 13:00 Rita Pardini (referente Schlesinger) (Università di Pisa) Aula Seminari F. Saleri VI Piano Dipartimento di Matematica Sistemi paracanonici di varieta di dimensione di Albanese massima. Abstract:Parlero di alcuni recenti risultati ottenuti in collaborazione con M. Mendes Lopes e G.P. Pirola. Sia X una varieta complessa liscia, con irregolarita q>0, sia D un divisore effettivo su X e sia H_D una famiglia irriducibile di divisori su X che domina Pic^D(X): si stabilisce un criterio coomologico affinche una curva D del sistema lineare |D| appartenga a H_D. Applicando questo criterio allo studio del sistema paracanonico principale di una varieta di tipo generale con applicazione di Albanese genericamente finita, si raffinano risultati di Beauville per le superfici e di Lazarsfeld-Popa in dimensione arbitraria. In particolare, in dimensione >2 si ottiene un inattesa disuguaglianza tra gli invarianti numerici di X, nell ipotesi che X non ammetta fibrazioni su varieta irregolari di tipo generale con applicazione di Albanese genericamente finita. 23/11/12 ore: 12:30 Riccardo Re (Università di Catania) Aula Seminari F. Saleri VI Piano Fibrati di parti principali su spazi proiettivi e rappresentazioni di quiver Abstract:I fasci di parti principali associati a fasci di moduli su schemi sono stati introdotti da Grothendieck nell ambito della geometria algebrica, ed essi costituiscono in questo contesto una generalizzazione dei jet bundles della geometria differenziale. Nonostante la loro ormai datata introduzione, fino a tempi molto recenti la struttura dei fibrati di parti principali associati ad un line bundle O(d) su uno spazio proiettivo, decisamente il caso più semplice dell intera teoria, non era stata ancora pienamente compresa. Il lavoro di cui parlerò colma questa lacuna, dando una descrizione di tali fibrati usando la loro omogeneità e la teoria delle rappresentazioni di quiver associate a fibrati omogenei. 21/06/12 ore: 14:30 Jasmin Raissy (Universita di Milano Bicocca) Aula Seminari 3 piano Operatori di Toeplitz e misure di Carleson in domini fortemente pseudoconvessi Abstract:Descriverò le proprietà degli operatori di Toeplitz associati ad una misura di Borel positiva finita definita su un dominio limitato fortemente pseudoconvesso $D subset subset C^n$. In particolare, otterremo condizioni ottimali sulla misura che assicurano che l operatore di Toeplitz associato mandi lo spazio di Bergman $A^p(D)$ in $A^r(D)$ con $r>p$, generalizzando e rendendo più precisi i risultati di Cuckovic e McNeal. Per ottenere tali condizioni, darò una caratterizzazione geometrica delle misure di Carleson e delle misure di Carleson vanishing su spazi di Bergman pesati in termini della geometria di Kobayashi intrinseca del dominio, generalizzando in questo ambito i risultati ottenuti da Kaptanoglu per la palla unitaria. (Lavoro in collaborazione con M. Abate e A. Saracco). 07/06/12 ore: 14:15 Gian Pietro Pirola (Università di Pavia) aula seminari terzo piano La superficie di Fano della cubica liscia e la sua funzione normale. Abstract:La superficie di Fano delle rette del cubico solido e stata utilizzata da Clemens e Griffiths per provare la non razionalita di ogni cubica liscia dello spazio proiettivo di dimensione 4. La superficie di Fano e una superficie irregolare estremamente interessante. Discutero il legame tra la sua geometria, il ciclo definito nella sua varieta di Albanese e la funzione normale da esso definita. I nuovi risultati sono stati ottenuti in collaborazione con A.Collino e J.C. Naranjo. 25/05/12 ore: 15:00 Alessandro Perotti (Università di Trento) Aula Seminari del 3 piano Formule di Cauchy di volume per funzioni slice regolari su *-algebre associative Abstract:Si introducono formule di Cauchy di volume per funzioni slice e funzioni slice regolari su una *-algebra reale associativa. Per ogni sottospazio opportuno dell algebra, si ottiene una formula di Cauchy, con dominio di integrazione contenuto nel sottospazio. In particolare, nel caso quaternionico si ottiene una formula di volume (quadridimensionale). Nel caso di un algebra di Clifford, la scelta del sottospazio dei paravettori corrisponde ad una formula di Cauchy (n+1-dimensionale) per le funzioni slice monogeniche. 17/05/12 ore: 14:30 Lucia Caporaso (Università  di Roma Tre) Aula Fausto Saleri sesto piano Teoria di Brill-Noether algebrica, combinatoriale e tropicale (nell ambito del seminario di Geometria algebrica organizzato congiuntamente al Dipartimento di matematica dell Università  di Milano). Abstract:Si descriveranno analogie e differenze tra la classica teoria di Brill-Noether per le curve algebriche, e la recente, e tuttora in fase di sviluppo, teoria di Brill-Noether per grafi e curve tropicali. Ci si concentrera sull interazione tra i diversi settori, descrivendo alcuni risultati recenti e qualche congettura. 03/05/12 ore: 14:30 Alberto Alzati (Università degli Studi di Milano) Aula seminari Mox sesto piano Trasformazioni Cremoniane generalizzate Abstract:In questo seminario saranno illustrate alcune parti di un recente lavoro svolto in collaborazione con J. C Sierra (ICMAT, Madrid) nel quale vengono studiate le applicazioni birazionali, con luogo base X liscio, ridotto ed irriducibile, tra uno spazio proiettivo, di dimensione arbitraria, ed una varietà di Fano di prima specie. Estendendo alcuni precedenti risultati di Crauder-Katz ed Ein-Shepherd Barron si ottiene una classificazione completa quando la dimensione di X è 1 o 2 e quando la codimensione di X è 2. In altri casi si ottengono risultati parziali. Nel seminario verrà posta particolare attenzione agli esempi che sono stati costruiti per dimostrare che la classificazione ottenuta è effettiva. 24/04/12 ore: 14:00 Luca Giuzzi (Università degli Studi di Brescia) Aula Seminari III piano Algebraic and geometric methods in cryptography Abstract:This talk will focus on the close interplay between some algebraic and geometric constructions and the actual realisation and analysis of efficient and robust cryptosystems. 24/04/12 ore: 14:45 Alexander Frolov (National Research University Moscow Power Engineering Institute) Aula Seminari III piano Effective Oblivious Transfer Using a Probabilistic Encryption Abstract:Some novel effective m-out-of-n interactive and non-interactive oblivious transfer protocols (OT protocols) using a probabilistic encryption are presented. Their key information is adapted from corresponding Bellare − Rivest fractional OT protocols and the encryption is carried out on ElGamal. They can be realized in a multiplicative as well as an additive group of prime order. It is shown that due to usage of different encryption keys this implementation can be simplified in such a way that single randomizer is sufficient for all encryptions. The proposal allows to increase the information rate by 2n/(n+1) times and to reduce by the same factor the computational complexity of the second round phase of interactive and of the communication phase of non-interactive m-out-of-n OT protocols explored probabilistic encryption. These propositions have potential applications in all cryptographic protocols based on the m-out-of-n oblivious transfer using probabilistic encryption including generalized oblivious transfer, in particular in electronic commerce. 19/04/12 ore: 15:00 Jacopo Stoppa (Università di Pavia) Aula seminari sesto piano Una formula di degenerazione per quiver e l equivalente in teoria di Gromov-Witten Abstract:Un quiver e un grafo orientato, i cui vertici corrispondono a spazi vettoriali, e i cui lati corrispondono ad applicazioni lineari. Esiste una ricca teoria che studia le geometria degli spazi dei moduli di quiver. Recentemente Manschot, Pioline e Sen (motivati da argomenti di teoria delle stringhe) hanno scoperto una notevole formula per il polinomio di Poincaré di tali spazi. Nel seminario discutero questo risultato e le sue interazioni con altre tecniche, per esempio la localizzazione. Infine mostrero come per un ampia classe di quiver esso sia equivalente a una ben nota formula di degenerazione per invarianti di Gromov-Witten che enumerano opportune curve razionali. Lavoro in collaborazione con M. Reineke e T. Weist. 13/04/12 ore: 14:30 Pavel Gumenyuk (Università di Roma Tor Vergata) Aula Fausto Saleri , 6 piano Loewner Theory: recent development in the classical topic Abstract:This theory was born in a paper by Ch. Loewner of 1923 as a tool in the famous Bieberbach Conjecture on the sharp estimates for the Taylor coefficients of univalent holomorphic functions in the disk. Loewner s dynamic viewpoint, going back to the Lie Theory, gave rise to a Parametric Representation of univalent functions in terms of a convex cone formed by measurable families of normalized holomorphic functions with positive real part. This representation was extensively used to solve extremal problems for univalent functions not accessible by other methods and actually served as the cornerstone in the proof of the Bieberbach Conjecture given by L. de Branges in 1984. After de Branges s proof, the interest to sharp estimates for univalent functions gradually decreased. However, Loewner s method has gone far beyond the original problem. Furthermore, recently there has been a burst of interest in this topic due to some new important results and applications, including well-celebrated O. Schramm s stochastic version of the Loewner evolution (SLE), deep results of S. Rohde, D. Marshall, and J. Lind on the relation between the analytic properties of the driving term in the Loewner equation and geometric properties of the represented conformal mapping, as well as interesting connections with Integrable Systems and Laplacian Growth. The first part of the talk we will be devoted to the basic constructions and ideas behind the classical Loewner Theory. The second part will focus on the new general approach by F. Bracci, M. Contreras and S. Díaz-Madrigal bringing together, and containing as quite particular cases, two similar but formerly independent variants of Loewner s construction (known as radial and chordal Loewner evolutions) along with one-parametric semigroups of holomorphic self-maps, which were studied for a long time separately in connection with the iteration theory and investigations of composition operators. Joint results with Professors M. Contreras and S. Díaz-Madrigal from the University of Seville, Spain, will be presented on the construction of the general Loewner chains and the relation between them and the non-autonomous holomorphic flows in the unit disk, produced by the general version of the Loewner-Kufarev equation. We will also discuss the extension of the general approach by Bracci et al. to doubly connected domains. The main difficulty we had to overcome in developing the general version of the Loewner Theory for the annulus resides in the necessity to switch from a static reference domain to a family of annuli, which excludes the possibility to consider autonomous reduction affording a good source of intuition in the simply connected case. 16/02/12 ore: 14:15 Filippo Bracci (Universita di Roma Tor Vergata) Aula seminari Fausto Saleri , VI piano Ed. La Nave Dinamica di semigruppi di mappe olomorfe del disco in se e comportamento al bordo Abstract:E ben noto che ogni semigruppo (continuo) di mappe olomorfe dal disco in se corrisponde ad un campo di vettori olomorfo semicompleto, detto generatore infinitesimale del semigruppo, e viceversa. Pertanto e naturale attendersi che le proprieta dinamiche del semigruppo siano collegate alle proprieta analitiche del suo generatore infinitesimale. In particolare, gli zeri del generatore infinitesimale corrispondono ai punti fissi del semigruppo, e questo e vero, con qualche cautela, anche per gli zeri al bordo del disco (dove gli elementi considerati non sono nemmeno continui in genere). In un recente lavoro con M. Contreras e S. Diaz-Madrigal, l oratore ha introdotto e studiato delle singolarita di tipo polo al bordo per il generatore infinitesimale e provato che, abbastanza sorprendentemente, queste corrispondono a punti del semigruppo con beta-numeri di Carleson-Makarov positivi, da cui si ottiene una naturale relazione con la congettura di Brennan. Lo scopo di questo seminario e di introdurre le idee sopra esposte per un pubblico con conoscenze di base di analisi complessa. 26/01/12 ore: 14:00 Paolo Lella (Università di Torino) aula seminari terzo piano Equazioni per lo schema di Hilbert Abstract:In questo seminario ripercorrerò la costruzione classica dello schema di Hilbert come sottoschema di una opportuna Grassmanniana e presenterò un nuovo modo di calcolare le equazioni che lo definiscono, descritte da Iarrobino-Kleiman e Bayer-Haiman-Sturmfels. Infine descriverò un nuovo tipo di equazioni di grado inferiore. Si tratta di un lavoro in collaborazione con Jerome Brachat, Bernard Mourrain e Margherita Roggero. 28/10/11 ore: 11:00 Tatiana Jajayacova (Comenius University and Rose-Hulman Institute of Technology) Aula seminari III piano Combinatorial structures with regular automorphism groups. Abstract:The concept of an automorphism group of a combinatorial structure is a fundamental concept in the cross-section of Combinatorics and Group Theory. Finding the automorphism group of a specific structure is a notoriously hard problem whose general complexity has not been resolved but it is believed to be exponential. In the talk, I will address the opposite problem of constructing a combinatorial structure for a given automorphism group. The left (or right) regular action of a group on itself is one of the most natural group actions to consider. The focus of our talk will be on combinatorial structures whose full automorphism groups act regularly on their sets of vertices. Equivalently, we discuss finite groups whose element sets admit the introduction of a combinatorial structure whose full automorphism group consists solely of the automorphisms induced by the multiplication by the elements of the underlying group. Such structures can be thought of as combinatorial representations of the corresponding groups. Previous results on this topic include the classification of graphical regular representations (graphs with regular automorphism groups), classification of digraphical regular representations (directed graphs with regular automorphism groups), as well as the classification of general combinatorial structures (incidence structures) with regular automorphism groups. We generalize these results to the class of k-hypergraphs which are incidence structures with all blocks of size k. 07/06/11 ore: 10:30 Roberto Notari (Dipartimento di Matematica, Politecnico di Milano) Aula seminari del terzo piano Una costruzione di schemi proiettivi ACM Abstract:Intendo presentare una costruzione di schemi proiettivi ACM di codimensione qualsiasi ed alcuni esempi per illustrarla. 12/05/11 ore: 14:30 Luca Ferrari (Dipartimento di Sistemi e Informatica, Firenze) Aula Seminari III piano The Moebius function of the consecutive pattern poset. Abstract:An occurrence of a consecutive permutation pattern $p$ in a permutation $pi$ is a segment of consecutive letters of $pi$ whose values appear in the same order of size as the letters in $p$. The set of all permutations forms a poset with respect to such pattern containment. We compute the Möbius function of intervals in this poset, providing what may be called a complete solution to the problem. For most intervals our results give an immediate answer to the question. In the remaining cases, we give a polynomial time algorithm to compute the Möbius function. In particular, we show that the Möbius function only takes the values -1, 0 and 1. 16/02/11 ore: 14:00 Ignacio Ojeda (Universidad de Extremadura, Spagna) Aula Saleri, VI piano Primary decomposition of binomial ideals Abstract:In the talk, I will deal with the problem of computing a binomial primary decomposition of binomial ideals. Moreover, I will discuss some applications. 07/06/10 ore: 14:30 Irene Sabadini (Dipartimento di Matematica Politecnico di Milano) aula Fausto Saleri (VI piano) Un introduzione alle funzioni slice-iperolomorfe Abstract:Introdurremo la recente nozione di slice-iperolomorfia, inquadrandola nel panorama delle nozioni piu classiche di olomorfia nel caso ipercomplesso. Mostreremo alcune proprieta delle funzioni slice iperolomorfe e ne presenteremo le applicazioni, ad esempio, al calcolo funzionale per operatori quaternionici e per n-uple di operatori lineari non necessariamente commutanti. 07/06/10 ore: 16:00 Pierluigi Moseneder (Dipartimento di Matematica Politecnico di Milano) aula Fausto Saleri (VI piano) Denominator formulas for superalgebras Abstract:The Weyl denominator identity is one of the most intriguing identities in the character ring of a complex finite dimensional simple Lie algebra. In this talk we are presenting expressions for the analog of the denominator identity in the case of a basic classical Lie superalgebra. Unlike the Lie algebra case, the denominator identity depends on the choice of the positive system. Kac and Gorelik provided formulas for a special class of positive systems. In our talk we will explore a case that is opposite to the ones studied by Kac and Gorelik: the so called distinguished case. Connections with Howe theory of dual pairs are also made. 15/03/10 ore: 15:00 Clelia De Felice (Università di Salerno) Aula seminari III piano Una survey sui sistemi splicing Abstract:Abstract Recombinant DNA (rDNA) is a general term which refers to the DNA resulting from the process of combining a piece of DNA, with another strand of DNA. In 1987 Tom Head pioneered a language-theoretic approach for studying recombinant DNA. He introduced the splicing systems, abstract models which are a formal counterpart of the DNA recombination under the action of restriction and ligase enzymes (gene splicing). In spite of a vast literature on splicing systems, briefly surveyed here, a few problems related to their computational power are still open. We intend to evidence how classical techniques and concepts in automata theory are a legitimate tool for investigating some of these problems. 04/02/10 ore: 14:00 Luca Migliorini (Università di Bologna) Aula seminari III piano Topologia della mappa di Hitchin e teoria di Hodge della varietà dei caratteri Abstract:Il sunto del seminario in formato pdf si trova in www1.mate.polimi.it/seminari/migliorini.pdf 14/01/10 ore: 11:00 Angelo Sonnino (Università della Basilicata) Aula seminari del terzo piano La geometria della sicurezza informatica e problemi connessi. Abstract:L implementazione di un criptosistema in una rete di comunicazione pone alcuni specifici problemi di natura matematica. In questa trattazione si discutono alcuni di questi problemi quali, nel caso di un criptosistema ellittico, l immersione dello spazio dei messaggi in una curva ellittica ed il calcolo del prodotto fra elementi di un campo di Galois di ordine elevato, con particolare riguardo all ottimizzazione per sistemi con limitata disponibilità di tempo per il trattamento dei dati. 18/12/09 ore: 14:00 Boris Melnikov (State University of Togliattigrad) auletta seminari III piano $A^{\omega}=B^{\omega}$ for $A$ and $B$ finite sets. 11/12/09 ore: 14:00 Boris Melnikov (State University of Togliattigrad) Aula seminari III piano Quick algorithms for state-minimization of finite automata 16/10/09 ore: 14:00 Boris Melnikov (Togliatti State University) Aula seminari Mox F.Saleri Non deterministic finite automata 02/07/09 ore: 14:00 Fernando Cukierman (Universidad de Buenos Aires) aula seminari del III piano Geometry of moduli spaces of foliations in projective spaces 25/05/09 ore: 14:30 Ignacio Ojeda Martinez de Castilla (Universidad de Extremadura) Aula interna, III piano Indispensable binomials in semigroup ideals 14/05/09 ore: 14:00 Eva Riccomagno (Universita degli Studi di Genova) Aula interna 7 piano A short history of algebraic statistics Abstract:Polynomials and ratios of polynomials appear in statistics and probability under various forms, in model representations as well as in inferential procedures. Algebraic geometry studies (ratios of) polynomials and the zeros set of systems of polynomial equations. Algebraic statistics uses techniques from (real) algebraic geometry, and commutative algebra, geometric combinatorics, ... to gain insight into the structure and properties of statistical models and to advise in model analysis. This, in turn, may prompt research in algebraic geometry. (Published in Metrika 2009 69:397-418) 12/05/09 ore: 14:00 Luca Ferrari (Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze) Aula seminari III piano Some combinatorics related to central binomial coefficients: Grand-Dyck paths, coloured noncrossing partitions and signed pattern avoiding permutations Abstract:Vengono studiate proprietà enumerative e d ordine di alcune strutture combinatorie contate dai coefficienti binomiali centrali. In particolare, vengono determinate nuove biiezioni fra cammini di Grand-Dyck e specifiche classi di permutazioni colorate a motivo escluso e si dimostra che i reticoli dei cammini di Grand-Dyck di lunghezza fissata sono isomorfi a determinati sottoinsiemi parzialmente ordinati dell ordine di Bruhat sulle permutazioni colorate che escludono specifici motivi, anch essi colorati. 31/03/09 ore: 12:30 Luca Giudici () Aula seminari MOX, VI piano Varietà di anelli *-regolari e/o ortoreticoli modulari associati alle logiche quantistiche di von Neumann. Abstract:Introduzione. Tralasciando pochissimi casi notoriamente patologici, von Neumann stabilì una equivalenza tra tre tipi di strutture matematiche usabili per descrivere quei sistemi fisici puramente quantistici in cui il calcolo algebrico tra osservabili (illimitati e non commutanti fra loro) è sempre possibile: (1) fattori finiti F; (2) geometrie continue con probabilità di transizione (astrattamente assimatizzate o costruite come ortoreticoli L delle proiezioni di un F); (3) l anello *-regolare R degli operatori (lineari chiusi e densamente definiti, ma possibilmente illimitati) affiliati ad F. (3) fornisce il calcolo algebrico su tutti gli osservabili del sistema fisico, (1) solo per quelli a spettro limitato, mentre (2) fornisce il calcolo proposizionale per tali logiche quantistiche di von Neumann. I problemi. (1) i fattori finiti nascono come generalizzazione dei fattori finito-dimensionali, ma già von Neumann ne diede esempi che non sono approssimativamente finito dimensionali , e dopo Connes conosciamo e classifichiamo una infinità continua di tali esempi tra loro non isomorfi. C è un qualche modo in cui tutti i fattori finiti possono essere ricondotti ai fattori finito dimensionali (cioè i normali *-anelli di matrici con coefficienti scalari)? (2) in un sistema classico, il calcolo proposizionale (algebra di Boole) è decidibile (mediante tavole di verità). Cosa accade per i sistemi quantistici? I risultati. L anello *-regolare R degli operatori (anche illimitati) affiliati a un fattore finito F (tra le algebre di von Neumann) è nella varietà generata dai fattori finito dimensionali. Analogamente generalizzando F a una C^*-algebra finita e di Rickart. Ne consegue che il calcolo proposizionale (l insieme delle tautologie) della logica quantistica di von Neumann è decidibile. Inoltre, i metodi (logico-algebrici) usati forniscono un nuovo punto di vista per il problema di immersione di Connes (1976) e il problema di Kaplansky sulla linearità delle (2-)quasitracce (1952). 27/03/09 ore: 10:30 Stefano Tebaldini (Politecnico di Milano, Dipartimento di Elettronica e Informazione) Dipartimento di Matematica, Sala Consiglio, VII piano Polarimetric SAR Tomography of Natural Scenarios: Current Achievements and Perspectives Abstract:SAR imaging is a well established technology for the remote sensing of the Earth’s surface. The rationale of such technology is to synthesize a virtual sensor array as long as several kilometers by flying a Radar sensor onboard an airborne or spaceborne platform, resulting in the possibility to produce a Radar image of the illuminated scene with a spatial resolution in the order of few meters. By jointly processing several SAR images, acquired along different paths, the capabilities of SAR imaging get enhanced by one dimension, therefore producing a 3D Tomographic reconstruction of the illuminated scene. Furthermore, modern SAR sensors are capable of transmitting and receiving all the different vector components (or polarizations) of the Electric field, resulting in the possibility to discriminate among different targets basing on electromagnetic diversity. In the last ten years, the availability of spatial and electromagnetic diversity within the data has been widely exploited in the analysis of forested areas, giving rise to the field of Polarimetric SAR Interferometry (PolInSAR). PolInSAR is today a well established technique, mostly used for the retrieval of the vegetation height above the ground basing on 2 multi-polarimetric SAR images. In this paper we outline a new technique for the joint exploitation of several multi-polarimetric SAR images, to the aim of yielding a separate tomographic reconstruction of each of the different objects (often referred to as Scattering Mechanisms) that contribute to the received signal. Such technique extends PolInSAR, and will be referred to as Polarimetric SAR Tomography (PolT-SAR). Under large hypotheses it will be shown that the data second order statistics can be expressed as a Sum of Kronecker Products (SKP) between two matrices, the first accounting for the electromagnetic properties and the second for the spatial structure of each of the Scattering Mechanism that contribute to the received signal. The key to the exploitation of the SKP structure is the existence of a technique for the decomposition of a matrix into a SKP. Such decomposition has the same formal properties as the SVD decomposition, the right and left singular vectors being replaced by two sets of matrices mutually orthogonal under the Frobenius inner product. As a consequence, the important result follows that, given the data covariance matrix, the K scattering mechanisms that contribute to the received signal are uniquely identified by K(K-1) real numbers. The implications of this result will be discussed from both the theoretical and the experimental point of view, showing the current achievements and outlining the future research perspectives. 27/03/09 ore: 11:30 Paolo Checchia (Istituto Nazionale di Fisica Nucleare sez. di Padova) Dipartimento di Matematica, Sala Consiglio, VII piano First results on material identification and imaging with a large-volume muon tomography prototype. Abstract:The muon tomography technique, based on the multiple Coulomb scattering of cosmic ray muons, has been proposed recently as a tool to perform non-destructive assays of large volume objects. Experimental results are reported from a large volume (about 11 m3) scanning system prototype, assembled using two large area CMS Muon Barrel drift chambers. The imaging capabilities of the system and the first measurements of the capability of the technique to discriminate among different materials are presented. 27/03/09 ore: 15:00 Birgit van Dalen (Leiden University) Dipartimento di Matematica, Sala Consiglio, VII piano On the difference between solutions of discrete tomography problems. Abstract:We consider the problem of reconstructing binary images from their horizontal and vertical projections. It is well-known that the reconstruction may not be uniquely determined, and that it is in fact possible to have two disjoint reconstructions from the same set of projections. We will present a condition that the projections must necessarily satisfy in order for this to happen. More general, we can derive from given projections an upper bound on the symmetric difference between two reconstructions. We will also consider reconstructions from two different sets of projections, which gives us new stability results for the case of two directions. 27/03/09 ore: 09:30 Francesca Cosmi (Universita di Trieste) Dipartimento di Matematica, Sala Consiglio, VII piano Application of synchrotron radiation micro-CT to local morphological and numerical characterization of short fibre reinforced polymer composites. Abstract:In components of short glass fibre reinforced polymer obtained by injection moulding, processing conditions produce complex orientation patterns that influence the mechanical properties of the component. Computed microtomography with synchrotron radiation constitutes the ideal analysis non destructive technique, being able to provide high resolution images of the internal structure of the material. In particular, the source high spatial coherence available at Elettra (Trieste) makes is possible to apply imaging techniques that exploit also information of the phase shifts induced by the sample inhomogeneities. These techniques are effective to detect even small details, such as short reinforce fibres within a polymeric matrix. Given fibre numerosity in our samples, instead of trying to isolate each single fibre and measure its geometrical properties from the 3D micro-CT reconstructions, we choose to compute global anisotropy parameters, commonly employed in other fields such as biomechanics or geology. Mean Intercept Length (MIL) and the related fabric tensor were used to assess local fibre orientation variations and to interpreter fatigue tests results in the light of different fibre orientation distributions. The problem of whether a morphological description can be predictive of the local elastic behaviour of these materials has also been addressed. 27/03/09 ore: 12:00 Franco Tomarelli (Politecnico di Milano, Dipartimento di Matematica) Dipartimento di Matematica, Sala Consiglio, VII piano Variational approach to image segmentation. Abstract:This talk deals with free discontinuity problems related to image segmentation, focussing on the mathematical analysis of Blake & Zisserman functional. Calculus of Variations is the framework where energy minimization and equilibrium notions find a precise language and formalizations by means of variational principles. Image segmentation is a relevant problem both in digital image processing and in the understanding of biological vision. There exist many different way to define the tasks of segmentation (template matching, component labelling, thresholding, boundary detection, quad-trees, texture matching, texture segmentation) and there is no universally accepted notion (optimality criteria for segmentation, analogies and differences between biological and automata perspective in segmentation): here the exposition is confined to some models for decomposing an image field, where is given a function describing the signal intensity associate to each point (typically the light intensity on a screen image). Such purpose has a clear connection with the problem of optimal partitions of a domain minimizing the length of the boundaries. In simple words the segmentation we look for provides a cartoon of the given image satisfying some requirements: the decomposition of the image is performed by choosing a pattern of lines of steepest discontinuity for light intensity, and this pattern will be called segmentation of the image. The variational formalizations of segmentation models provided deeper understanding of image analysis, produced intriguing mathematical questions (some of them still open) and entailed global estimates for geometric quantities in visual and automatic perception at both low and high level vision. We discuss some recent results based on the innovative notion of free discontinuity problem introduced by Ennio De Giorgi. This approach balances carefully signal smoothing and segmentation length. In such framework, modern tools of Geometric Measure Theory and recent developments about minimal surfaces and regularity of extremals in Calculus of Variations allow the study of problems coupling bulk and surface terms: in such context discontinuous (in the mathematical sense) solutions are admissible and sometimes their discontinuities are the main features of the solution. 27/03/09 ore: 14:00 Alain Daurat (Universite Louis Pasteur of Strasbourg) Dipartimento di Matematica, Sala Consiglio, VII piano Using Tomography in Digital Plane to solve problems of Geometric Tomography. Abstract:In this talk we will study the problem of determining in a constructive way a convex body in the plane from its tomographic projections. For this, we consider the similar problem in digital plane: reconstructing a lattice convex set from its discrete tomographic projection. We show that we can use a reconstruction algorithm for the discrete problem to solve the continuous reconstruction to any precision. The proof of this result uses stability properties of geometric tomography. An extension to point-source tomographic projections is also investigated. 27/03/09 ore: 15:30 Guido Musso (sub for Cesare Comina) (Politecnico di Torino) Dipartimento di Matematica, Sala Consiglio, VII piano Monitoring processes in soil laboratory samples with 3D electrical tomography Abstract:The talk will focus on the use of Electrical Resistivity Tomography as an imaging tool for the investigation of the hydro-mechanical behaviour of soil samples. In soil mechanics laboratory measurements are mostly performed from the boundaries of the soil samples, or anyway on a portion of sample that as a first approximation is assumed to behave homogeneously. Nevertheless, due to the inherent structure of the soil and to the non linearity of hydro-chemo-mechanical processes, several different phenomena can occur perturbing the assumed homogeneity (localization of mechanical strains, hydro-chemical dispersion, saturation – desaturation processes and so on). The interpretation of experimental evidences involving such phenomena is therefore complicated if measurements are taken in the traditional way. The use of 3D electrical tomography therefore has been investigated, in a dedicated advanced hydro-chemo-mechanical cell, in a number of experiments, both to reconstruct initial heterogeneities (e.g. due to local variations of porosity or mineralogy) or to monitor transient processes in homogeneous and heterogeneous soil conditions. Good results have been obtained for different phenomena such as mechanical consolidation, chemical diffusion and saturation changes. Preliminary exercises would suggest that the technique can be used in the quantitative characterization of sample properties, provided its association with numerical simulations of ‘multiphysics’ processes. This can be done by relating the soil electrical conductivity to structural and environmental soil conditions (porosity, water saturation and salt concentration in the pore water) by means of known transport laws. 26/03/09 ore: 16:30 Stefano Brocchi (Universita di Firenze) Dipartimento di Matematica, Sala Consiglio, VII piano Solving some instances of the two color problem. Abstract:The two color problem is an open problem in the field of discrete tomography, and it consists in determining a matrix, whose elements are of three different types, starting from its horizontal and vertical projections. It is known that the one color problem has a polynomial time reconstruction algorithm, while, with k > 2, the k-color problem is NP-complete. Thus, the two color problem constitutes an interesting example of a problem in the frontier between hard and easy problems. In this talk we describe a linear time algorithm to solve a set of its instances, where some values of the horizontal and vertical projections are constant, while the others are upper bounded by a positive number proportional to dimension of the problem. Our algorithm relies on classical studies for the solution of the one color problem. 26/03/09 ore: 15:00 Peter Gritzmann (Technische Universität München) Dipartimento di Matematica, Sala Consiglio, VII piano On Some New Results in Discrete Tomography. Abstract: Discrete tomography deals with the reconstruction of finite sets from knowledge about their interaction with certain query sets. The most prominent example is that of the reconstruction of a finite subset $F$ of $mathbb{Z}^d$ from its X-rays (i.e., line sums) in a small positive integer number $m$ of directions. Applications of discrete tomography include quality control in semiconductor industry, image processing, scheduling, and statistical data security. The reconstruction task is an ill-posed discrete inverse problem, depicting (suitable variants of) all three Hadamard criteria for ill-posedness. After a short introduction to the field of discrete tomography, the first part of the talk addresses the following questions. Does discrete tomography have the power of error correction? Can noise be compensated by taking more X-ray images, and, if so, what is the quantitative effect of taking one more X-ray? Our main theoretical result gives the first nontrivial unconditioned (and best possible) stability result. On the algorithmic side we show that while there always is a certain inherent stability, the possibility of making (worst-case) efficient use of it is rather limited. The second part of the talk deals with the discrete tomography of quasicrystals that live on finitely generated $Z$-modules in some $R^s$. Focussing on aspects in which the discrete tomography of quasicrystals differs from that in the classical lattice case, we solve a basic decomposition problem for the discrete tomography of quasicystals. More generally, we study the problem of existence of pseudodiophantine solutions to certain systems of linear equations over the reals and give a complete characterization of when the index of Siegel grids is finite. The results on stability are joint work with Andreas Alpers, that on Siegel grids are joint work with Barbara Langfeld. 26/03/09 ore: 16:00 Andreas Alpers (Technical University of Denmark) Dipartimento di Matematica, Sala Consiglio, VII piano Discrete Tomography and Imaging of Polycrystalline Structures Abstract:High resolution transmission electron microscopy is commonly considered as the standard application for discrete tomography. While this has yet to be technically realized, new applications with a similar flavor have emerged in materials science. In our group at Risø DTU (Denmark s National Laboratory for Sustainable Energy), for instance, we study polycrystalline materials via synchrotron X-ray diffraction. Several reconstruction problems arise, most of them exhibit inherently discrete aspects. In this talk I want to give a concise mathematical introduction to some of these reconstruction problems. Special focus is on their relationship to classical discrete tomography. Several open mathematical questions will be mentioned along the way. 12/03/09 ore: 10:30 Renzo Cavalieri (Colorado State University, Fort Collins) Aula Fausto Saleri, VI piano Congetture di Faber e non Abstract:In questo talk faro una panoramica su delle famose congetture di Carel Faber circa la struttura algebrica dell anello tautologico dello spazio di moduli di curve. Presenterò poi lavoro recente con Stephanie Yang in cui proponiamo naturali estensioni delle congetture di Faber. 06/03/09 ore: 11:00 Caterina Stoppato (Universita di Firenze) Edificio La Nave via Bonardi 9, Milano, aula interna 6 piano Singolarità di funzioni quaternioniche regolari 10/02/09 ore: 00:00 Elena V. Pribavkina (Ural State University - Ekaterinburg - Russia) Aula seminari III piano Slowly Synchronizing Automata with Zero and Incomplete Sets Abstract:Using combinatorial properties of incomplete sets in a free monoid we construct a series of $n$-state deterministic automata with zero whose shortest synchronizing word has length $\frac{n^2}4+\frac{n}2-1$. 26/01/09 ore: 11:00 Andrea Bernasconi (Mechanical Department, Politecnico of Milano Via La Masa 1, 20156 Milano MI) Aula Seminari III piano Resistenza e anisotropia in compositi rinforzati con fibre corte: analisi mediante tomografia con luce di sincrotrone Abstract:In questa memoria vengono presentati i risultati preliminari di una ricerca volta a misurare l’orientamento delle fibre di rinforzo in un materiale composito a matrice polimerica ottenuto con il processo dello stampaggio a iniezione. La caratterizzazione della microstruttura proposta utilizza un parametro, il Mean Intercept Length (MIL), comunemente impiegato in biomeccanica, ricavato da immagini tridimensionali ottenute mediante tomografia con luce di sincrotrone. La ricostruzione dell’immagine tridimensionale da una serie di radiografie premette di visualizzare la distribuzione spaziale delle fibre di vetro all’interno della fase polimerica. I risultati presentati si riferiscono ad un campione di poliammide 6 rinforzata con il 30% in peso di fibre corte di vetro, estratto da una lastra sottile stampata in modo da favorire lo sviluppo della tipica struttura a strati, caratterizzata da un orientamento delle fibre parallelo al flusso d’iniezione negli strati prossimi alle superfici e perpendicolare al flusso nella zona centrale. Una seconda serie di misure ha interessato campioni dello stesso materiale di geometria più complessa (lastrine con riduzione di sezione raccordata), caratterizzati da un comportamento meccanico differente al variare della posizione del punto d’iniezione, attribuibile ad una differente disposizione delle fibre di rinforzo. Le misure di MIL effettuate si sono rivelate in grado di fornire una stima del grado di anisotropia del materiale e di cogliere le differenze di orientamento delle fibre osservate nei differenti punti e strati del campione. 15/01/09 ore: 11:00 Guglielmo Lunardon (Università degli Studi di Napoli Federico II) Aula seminari MOX, VI piano del Dipartimento di Matematica Francesco Brioschi , Politecnico di Milano, via Bonardi n. 9 (edificio La Nave ) Semicorpi finiti Abstract:Il cubical array , introdotto da Knuth nel 1964, permette di costruire sei diversi semicorpi modificando opportunamente la moltiplicazione di un dato semicorpo finito. Tale costruzione è stata oggetto di un rinnovato interesse da parte di vari autori per i legami tra i semicorpi commutativi e le fibrazioni simplettiche. In questa comunicazione si caratterizzano i nuclei dei sei semicorpi ottenuti mediante il cubical array e si presentano alcuni recenti risultati sulla loro struttura. 21/11/08 ore: 00:00 Akihiro Yamamura (Akita University) Aula Seminari F.Saleri , VI Piano, Dip.Mat. Automata theoretic methods in inverse semigroups 05/09/08 ore: 00:00 Juhani Karhumaki (Università di Turku-) aula seminari III piano Dipartimento di Matematica "Connections between words and matrices". Abstract:There is well known connection between words and integer matrices known already almost hundred years stating that free monoids (finitely or countably generated) can be embedded into the multiplicatice semigroup of matrices. This allows in one hand to conclude simple undecidablity results for matrices, and on the other hand some weak dimension properties for words. These and related results are analyzed in this lecture. 27/05/08 ore: 00:00 Sinisa Crvenkovic (University of Novi Sad) Aula Seminari III piano Church-Turing thesis in algebra Abstract:We will present examples of varieties of algebras having solvable word problems and undecidable equational theory. 27/05/08 ore: 15:00 Sinisa Crvenkovic (University of Novi Sad) aula seminari III piano Church-Turing thesis in algebra Abstract:We will present examples of varieties of algebras having solvable word problems and undecidable equational theories. 09/04/08 ore: 14:00 Arrigo Bonisoli (Dipartimento di Scienze e Metodi dell Ingegneria, Università di Modena e Reggio Emilia) Aula seminari del III piano del Dipartimento di Matematica Francesco Brioschi , Politecnico di Milano, via Bonardi n. 9 (edificio La Nave ) Decomposizioni di grafi Abstract:Consideriamo solo grafi semplici (non orientati, privi di cappi e spigoli multipli). Nella sua accezione più generale una decomposizione di un asegnato grafo T non è altro che una famiglia di sottografi di T, a due a due privi di spigoli comuni, che ricoprono l insieme degli spigoli di T. In buona sostanza i sottografi della decomposizione danno luogo a una partizione dell insieme degli spigoli del grafo T. Un caso molto studiato è quello in cui i sottografi della decomposizione sono tutti isomorfi a un assegnato grafo G; in questo caso si parla di una G-decomposizione di T. Quando T è il grafo completo su v vertici una G-decomposizione di T viene anche indicata come G-disegno. La dicitura è giustificata dal fatto che, come per i disegni classici, per due punti continua a passare un unico blocco, solo che questo blocco ha la forma del grafo G. Nel presente seminario esporrò alcuni risultati vecchi e nuovi nel caso in cui T è il grafo completo K_v, assumendo l esistenza di un gruppo di automorfismi della G-decomposizione con proprietà assegnate. Gli ultimi contributi riguardano il caso in cui G è un grafo di Petersen (generalizzato) o un matching di cardinalità k. 22/02/08 ore: 10:30 Flavio d Alessandro (Dip. di Matematica, Roma la Sapienza) Aula seminari MOX La Congettura di Cerny Abstract:Lo scopo di questo seminario e' quello di presentare una survey, di natura introduttiva, su di una ben nota congettura di Informatica teorica riguardante gli automi sincronizzanti. Un automa deterministico si dice sincronizzante se esistono una parola w sul suo alfabeto di ingresso ed un suo stato q tali che, comunque si consideri uno stato p dell'automa, lo stato da esso raggiunto, leggendo la parola w, a partire da p, e' lo stato q. La parola w e lo stato q sono detti rispettivamente parola e stato di reset. Una famosa congettura formulata da Cerny nella seconda meta' degli Anni 60 stabilisce che ogni automa sincronizzante avente n stati possiede una parola di reset di lunghezza inferiore o uguale a (n-1)^{2}. In questo seminario, dopo aver delineato il quadro storico e le motivazioni che rendono significativo lo studio del problema, presenteremo alcune famiglie notevoli di automi sincronizzanti ed alcune idee soggiacenti alle tecniche utilizzate per tale studio. 22/02/08 ore: 10:30 Flavio d Alessandro (Dipartimento di Matematica Guido Castelnuovo , Universita di Roma La Sapienza) Aula seminari MOX del VI piano del Dipartimento di Matematica Francesco Brioschi , Politecnico di Milano, via Bonardi n. 9 (edificio La Nave ) La congettura di Cerny Abstract:Lo scopo di questo seminario è quello di presentare una survey, di natura introduttiva, su di una ben nota congettura di Informatica teorica riguardante gli automi sincronizzanti. Un automa deterministico si dice sincronizzante se esistono una parola w sul suo alfabeto di ingresso ed un suo stato q tali che, comunque si consideri uno stato p dell automa, lo stato da esso raggiunto, leggendo la parola w, a partire da p, è lo stato q. La parola w e lo stato q sono detti rispettivamente parola e stato di reset. Una famosa congettura formulata da Cerny nella seconda metà degli Anni 60 stabilisce che ogni automa sincronizzante avente n stati possiede una parola di reset di lunghezza inferiore o uguale a (n-1)^2. In questo seminario, dopo aver delineato il quadro storico e le motivazioni che rendono significativo lo studio del problema, presenteremo alcune famiglie notevoli di automi sincronizzanti ed alcune idee soggiacenti alle tecniche utilizzate per tale studio. 03/12/07 ore: 11:30 Davide Schipani (Università di Zurigo) Aula seminari MOX del VI piano del Dipartimento di Matematica Francesco Brioschi , Politecnico di Milano, via Bonardi n. 9 (edificio La Nave ) Il problema della conservazione sicura dei dati biometrici Abstract:Ai fini dell autenticazione è oggi sempre più diffuso l utilizzo di caratteristiche intrinseche all individuo, quali l impronta digitale, l iride, il fondo della retina, etc... Al contrario delle password alfanumeriche tradizionali, per quelle biometriche è prevista una tolleranza fino a una determinata soglia d errore. Questo tuttavia pone problemi rilevanti in riferimento all immagazzinamento sicuro di tali dati. Le prime idee chiave per ovviare al problema, basate sull uso dei codici correttori d errore, risalgono alla fine degli anni novanta, con il fuzzy commitment scheme di Juels e Wattenberg. Tuttavia questo e i successivi sviluppi lasciano un campo di ricerca ancora ricco e aperto, soprattutto per le difficoltà che si presentano a livello pratico nel mondo reale. 30/10/07 ore: 00:00 Renzo Sprugnoli (Universita degli Studi di Firenze) Dip. di Matematica F. Brioschi Il metodo dei coefficienti e le sue applicazioni Abstract: Verranno esposte le proprietà basilari del metodo dei coefficienti, per la manipolazione delle successioni numeriche e delle loro funzioni generatrici. Allo scopo, verrà proposto un metodo assiomatico che permette la costruzione di funzioni generatrici e l'estrazione dei loro coefficienti, per la soluzione esatta o asintotica di problemi combinatori. La teoria verrà esposta insieme ad opportuni esempi, alcuni elementari, altri più complessi, di carattere generale o relativi a specifiche problematiche di ricerca. 08/10/07 ore: 11:00 Elisabetta De Bernardi (Dipartimento di Bioingegneria-Politecnico di Milan) Aula seminari-terzo piano Ottimizzazione di metodi iterativi a massima verosimiglianza per recupero di risoluzione in PET 14/06/07 ore: 00:00 Elena Pribavkina (Ural State University) Aula seminari III piano 2-­Collapsing Words And A Sequence Reconstruction Problem Abstract:Some recent results on reconstruction of a word by its inner factors will be presented. The reconstruction can be used in the behaviour of 2-collapsing words. 27/04/07 ore: 11:00 Joseph Zaks (University of Haifa , Haifa (Israel)) Aula Seminari del III piano del Dipartimento di Matematica Francesco Brioschi , Politecnico di Milano, via Bonardi n. 9 (edificio La Nave ) A few short combinatorial proofs in Geometry Abstract:We will treat the unit-distance graph over the real (or rational) points in Ed, discuss their connectivity and chromatic numbers, and use it in connection with the Beckman-Quarels Theorem ( Every mapping from Ed to itself, d >= 2, that preserves distance one is an isometry ). We will show that every closed curve on the unit sphere in E^d that meets all the d major hyperplanes has length of at least pi. 30/03/07 ore: 11:00 Aljosa Volcic (Universita della Calabria) Sala Consiglio VII piano Ricostruzione di corpi convessi da sezioni e proiezioni 30/03/07 ore: 12:00 Giuseppe Baselli (Dipartimento di Bioingegneria, Politecnico di Mila) Sala Consiglio VII piano Ottimizzazione di metodi iterativi a massima verosimiglianza per recupero di risoluzione in PET 30/03/07 ore: 14:30 Elena Barcucci (Universita di Firenze) Sala Consiglio VII piano Tomografia Discreta: problemi, modelli, algoritmi 30/03/07 ore: 15:30 Alfio Quarteroni (Politecnico di Milano – EPFL Lausanne) Sala Consiglio VII piano La modellistica fra ricostruzione geometrica e simulazione 22/09/06 ore: 00:00 Boris Schein (University of Arkansas) Aula seminari III piano Constructions of free inverse semigroups Abstract:Differents constractions of free inverse semigroups are presented and the advantes and disvantages of all of them are compared. 20/03/06 ore: 00:00 Douglas Rogers (Univ. of Hawaii and Univ. of Bergen) CNR - IMATI, via Bassini, 15, Milano Bounds Archimedes missed: exercises in geometric extrapolation Abstract: Pi is a topic of abiding fascination that engages the interest of all mathematicians, pure and applied alike. We know, or think we know, that it was Archimedes who early calculated pi to considerable accuracy by bounding a circle inside and out by regular polygons. However, this program, with an explicit argument in the case of inscribed polygons, is already contained in Book XII of Euclid's Elements. Closer examination of the works of Euclid and of Archimedes suggests that everything you can do with inscribed and circumscribed polygons together can be done just as well with inscribed polygons alone. Moreover, it seems that the Chinese mathematician Liu Hui, working over seventeen hundred years ago, was able to improve the lower bound on the area of a circle by interpolation using only inscribed polygons. Perhaps even more surprisingly, whereas the combined work of Euclid and Archimedes shows that the difference between areas of circumscribed and inscribed polygons more than halves on doubling the number of sides of these polygons, an argument that would have been accessible to both of them, as well as to Liu Hui, shows that, in fact, it more than quarters. The talk is presented as an exercise in ''mathematics from history'', where we take the mathematics from a given period and see what (more) can be extracted by means of it alone. Thus, when we look back on this material from the later perspective of the calculus, we find that these geometric arguments remarkably powerful, giving results akin to Richardson-Romberg integration - the quartering inequality just mentioned is accurate up to the term in the sixth power of the reciprocal of the number of sides of the largest and smallest polygons. It seems that we - not just Archimedes - might have been missing something. 22/02/06 ore: 14:30 Chu Wenchang (Università degli Studi di Lecce) CNR, Milano Hypergeometric Approach to Weideman's Conjecture 21/02/06 ore: 00:00 Chu Wenchang (Univ. degli Studi di Lecce) Dip. di Matem. F. Brioschi The Cauchy Double Alternant and Divided Differences Abstract: As an extension of Cauchy's double alternant, we establish a general determinant evaluation formula. Several interesting determinant identities are derived as consequences by means of divided differences. 09/02/06 ore: 00:00 Simone Rinaldi (Univ. di Siena) CNR - IMATI, via Bassini 15, Milano Enumerazione di poliomini che pavimentano il piano Abstract: Beauquier and Nivat introduced and gave a characterization of the class of pseudo-square polyominoes, i.e. those polyominoes that tile the plane by translation: a polyomino tiles the plane by translation if and only if its boundary word W may be factorized as W = XYXY. We consider the subclass PSP of pseudo-square polyominoes which are also parallelogram. By using the Beauquier-Nivat characterization we provide by means of a rational language the enumeration of the subclass of psp-polyominoes with a fixed planar basis according to the semi-perimeter. The case of pseudo-square convex polyominoes is also analyzed. 29/11/05 ore: 11:00 Douglas Rogers (University of Tasmania) Dipartimento di Matematica - Politecnico di Milano Zero-one evaluations for the classic non-associative bracketing problem. 08/11/05 ore: 00:00 Mario Valencia-Pabon (Univ. de los Andes, Colombia) Dip. di Matem. F. Brioschi Independence and colorings properties of the direct product of powers of cycles 18/02/05 ore: 11:00 Chu Wenchang (Università degli Studi di Lecce) Dipartimento di Matematica - Politecnico di Milano Harmonic Number Identities and Hermite-Padè Approximations to the Logarithm Function 17/02/05 ore: 11:00 Chu Wenchang (Università degli Studi di Lecce) CNR, Milano Theta Function Identities and Ramanujan's Congruences on Partition Function 10/12/04 ore: 10:30 Tudor Zamfirescu (Universität Dortmund, Germany) Dipartimento di Matematica - Politecnico di Milano Intersecting longest cycles and paths 09/11/04 ore: 15:00 Renzo Sprugnoli (Università degli Studi di Firenze) Dipartimento di Matematica - Politecnico di Milano Riordan arrays e somme combinatorie 22/10/04 ore: 14:00 Vincenzo Marra (Università degli Studi di Milano) Dipartimento di Matematica - Politecnico di Milano Il Teorema dei Quattro Colori e triangolazioni canoniche della sfera. 20/07/04 ore: 11:00 Douglas Rogers (University of Tasmania) Dipartimento di Matematica - Politecnico di Milano Some problems in the enumeration of polyominoes 12/05/04 ore: 14:30 Douglas Rogers (University of Tasmania) CNR, Milano Dissecting the Pythagorean proposition 29/03/04 ore: 17:00 Richard Gardner (Western Washington University) Dipartimento di Matematica - Politecnico di Milano Algorithms for Reconstructing Shapes from Support-Type Function 25/11/03 ore: 11:00 Angelo Sonnino (Università della Basilicata) Dipartimento di Matematica - Politecnico di Milano Nuove tendenze in crittografia 21/11/03 ore: 00:00 Alexander Frolov (Moscow Power Engineering Univ., Moscow) Dip. di Matem. F. Brioschi , Pol. di Milano Expert systems for decision-making (verification, synthesis, time estimation) 07/10/03 ore: 00:00 Elena Barcucci (Univ. degli Studi di Firenze) Dip. di Matem. F. Brioschi , Pol. di Milano Tomografia discreta Abstract: Programma: Algoritmi per la ricostruzione di poliomini convessi a partire dalle loro proiezioni orizzontali e verticali. Martedì 7 Ottobre, ore 11.00 - aula seminari 3o piano. Sunto. Verranno presentati due algoritmi polinomiali per la ricostruzione di poliomini convessi (cioé poliomini le cui righe e colonne sono connesse). Il primo algoritmo è basato su alcune semplici operazioni che vengono applicate a righe e colonne e sull’eventuale riduzione al problema della 2-soddisfacibilità e si dimostra che se esiste un poliomino che soddisfa le proiezioni date questo viene sempre individuato. L’altro algoritmo utilizza ancora le stesse operazioni su righe e colonne ma in più si avvale di alcune proprietà sulle mediane di insiemi discreti. Questo consente di ridurre la complessità, ma non è dimostrato che l’algoritmo individui sempre la soluzione, anche se questo si è verificato sempre nelle prove eseguite. Problemi di ambiguita nella ricostruzione di insiemi discreti a partire dalle loro proiezioni. Martedì 7 ottobre, ore 15.00 - aula seminari 3o piano. Sunto. Verrà esaminato il problema dell’unicità della soluzione per la ricostruzione di insiemi discreti a partire dalle loro proiezioni. Verranno considerate diverse classi di insiemi discreti ottenute imponendo alcune proprietà quali connessione, convessità, ... inviduando le proprietà e gli insiemi di proiezioni che garantiscono l’unicità della soluzione. Verrà inoltre presentata una congettura secondo la quale 4 proiezioni, scelte opportunamente, sono sufficienti per avere l’unicità dei poliomini convessi, mostrando anche un programma che è stato utilizzato per ottenere una verifica sperimentale della congettura. Ricostruzione di insiemi discreti per mezzo di proiezioni con assorbimento. Mercoledì 8 ottobre, ore 11.00 - aula seminari 3o piano. Sunto. In alcuni recenti lavori, A. Kuba e M. Nivat hanno introdotto un modello di proiezioni con assorbimento. In questo caso le proiezioni lungo una direzione non sono più date dal numero di punti che si trovano sulle rette parallele alla direzione stessa ma da somme pesate mediante dei coefficienti. Nel caso che questi soddisfino una ricorrenza analoga a quella dei numeri di Fibonacci, gli autori mostrano che le proiezioni orizzontali e verticali non sono sufficienti a garantire l’unicità della soluzione. Verrà invece mostrato che le sole proiezioni orizzontali, considerate però nei due versi, sono sufficienti per garantire l’unicità e permettono anche di definire un algoritmo di ricostruzione lineare. 26/09/03 ore: 11:30 Pierre Leroux (Université du Québec a Montréal) Dipartimento di Matematica - Politecnico di Milano Emumerative problems inspired by Mayer's theory of cluster integrals in thermodynamics. 18/09/03 ore: 00:00 Chu Wenchang (Univ. degli Studi di Lecce) CNR, via Bassini 15, Milano Faà di Bruno formula and determinantal identities 27/06/03 ore: 11:00 Paolo Dulio (Politecnico di Milano) Dipartimento di Matematica - Politecnico di Milano Problemi di unicità in tomografia geometrica. 30/05/03 ore: 00:00 Helmut Karzel (Technische Universitat, Munchen) Dip. di Matem. F. Brioschi , Pol. di Milano La Geometria delle Riflessioni 15/04/03 ore: 15:00 Douglas Rogers (University of Tasmania) CNR di Milano Enumerative Combinatorics: Mathematics or Higher Numerology? 03/04/03 ore: 11:00 Andrea Scagliola (Politecnico di Milano) Dipartimento di Matematica - Politecnico di Milano Funzioni generalizzate: un approccio algebrico. 28/02/03 ore: 11:30 Giovanni Ferrero (Università di Parma) Dipartimento di Matematica - Politecnico di Milano Questioni naturali (mica tanto) elementari che nascono dai quasi-anelli. 11/12/08 ore 14 Riccardo Re (Università di Catania) Aula C del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Matrici nilpotenti a coefficienti polinomiali 25/11/08 Riccardo Re (Università di Catania) Edificio "La Nave" via Bonardi 9, Milano, aula interna 3 piano Immersioni aritmeticamente Cohen-Macaulay di curve che ammettono due fasci indipendenti di divisori 26/06/08 Chad Schoen (Duke University) Aula C del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 A family of surfaces constructed from genus 2 curves 24/06/08 Chad Schoen (Duke University) Aula C del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Calabi Yau threefolds with vanishing third Betti number 08/05/08 Jose Carlos Sierra (Universidad Complutense de Madrid) Aula dottorato del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Una limitazione inferiore del grado di un fibrato vettoriale globalmente generato 03/04/08 Francesco Polizzi (Universita' della Calabria) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Fibrazioni isotriviali standard e superfici di tipo generale con chi=0 25/02/08 Uli Schlickewei (Universite' de Nice) Aula C del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Moltiplicazione reale su superfici K3 e rivestimenti doppi di P2 22/01/08 Xavier Roulleau (Universita' di Angers) Aula C del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Elliptic curve configurations on Fano surfaces 17/12/07 Rebecca Goldin (George Mason and Cornell, USA) Edificio "La Nave" Via Bonardi 9, Milano, Aula interna 3 piano Introduction to toric varieties via symplectic geometry and orbifolds 15/11/07 Michele Bolognesi (Scuola Normale Superiore, Pisa) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Spazi osculatori ed equazioni diofantee 8/11/07 Letterio Gatto (Politecnico di Torino) Aula dottorato del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Calcolo di Schubert (anche equivariante) 11/10/07 Cristiano Bocci (Universita' di Milano) Aula dottorato del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Il ruolo dei punti grassi nel risorgimento degli ideali 24/09/07 Keiji Oguiso (University of Tokyo) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Connecting certain rigid birational non-homeomorphic Calabi-Yau threefolds via Hilbert scheme 26/06/07 Elham Izadi (Università della Georgia, Athens, USA) Edificio "La Nave" Via Bonardi 9, Milano, Aula interna 3 piano New correspondences on curves 01/06/07 Shigeru Mukai (RIMS di Kyoto) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Cohomologically trivial endomorphisms of Enriques surfaces 15/05/07 Fabrizio Andreatta (Universita' di Milano) Aula C di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Sottovarieta' localmente simmetriche nel luogo di Torelli 09/05/07 Robin Hartshorne (University of California at Berkeley) Aula 8, Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Gorenstein liaison of projective varieties 24/04/07 Antonio Laface (Universita' di Conception, Cile) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Cox ring of a projective space blown up along points 20/03/07 Carla Novelli (Universita' di Genova) Aula C, Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Varieta' unirigate da rette 15/03/07 Cristina Martinez (Universita' di Madrid) Aula C, Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Mirror simmetry and derived category 06/03/07 Giuseppe Pareschi (Universita' di Roma II Tor Vergata) Aula C, Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Generic vanishing e trasformate di Fourier Mukai 21/12/06 Massimiliano Mella (Universita' di Ferrara) Aula dottorato del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Proiezione tangenziale 18/12/06 Cinzia Casagrande (Universita' di Pisa) Edificio "La Nave" Via Bonardi 9, Milano, Aula interna 6 piano Introduzione alle varieta' toriche, II 11/12/06 Cinzia Casagrande (Universita' di Pisa) Edificio "La Nave" Via Bonardi 9, Milano, Aula interna 6 piano Introduzione alle varieta' toriche, I 04/05/06 Alessio Corti, (Imperial College) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Fano 3-folds and quantum cohomology 27/04/06 Tetsuji Shioda (Rikkyo University) Edificio "La Nave" Via Bonardi 9, Milano, Aula interna 3 piano Q-split models of rational elliptic surfaces 06/04/06 Marco Manetti (Universita' "La Sapienza" di Roma) Aula dottorato del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 L'applicazione dei periodi universale come morfismo L_{\infty} 30/03/06 Daniel Huybrechts (Universita' di Bonn) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Derived versus abelian equivalence of K3 surfaces 01/03/06 Rita Pardini (Universita' di Pisa) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Il gruppo fondamentale delle superfici con K^2 piccolo 09/02/06 Mario Valenzano (Universita' di Torino) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Sugli spazi lineari contenuti in una varieta' intersezione completa 02/02/06 Matthias Schuett (Universita' di Hannover) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Calabi-Yau threefolds as fibre products of elliptic surfaces 19/01/06 Alessandra Sarti (Universita' di Mainz) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Nikulin involutions on K3 surfaces 19/12/05 Philippe Ellia (Università di Ferrara) Edificio "La Nave" Via Bonardi 9, Milano, Aula interna 3 piano Sulle sottovarietà di codimensione due in P^n 08/11/05 A. Ikeda (Università di Osaka) Edificio "La Nave" Via Bonardi 9, Milano, Aula interna 3 piano Algebraic cycles on Jacobian varieties over function fields 28/10/05 Paltin Ionescu (Universita' di Bucarest) Aula C del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 On defective varieties 27/10/05 Alessandro Ghigi (Universita' di Milano-Bicocca) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Orbifold di Kaehler-Einsten e metriche di Einsten sulle sfere esotiche 20/10/05 Lidia Stoppino (Universita' di Pavia) Aula dottorato del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Una limitazione inferiore ottimale per la slope di fibrazioni doppie 06/10/05 Alessandra Sarti (Università di Mainz) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Transcendental lattices of some special families of K3-surfaces 15/09/05 Masa-Hiko Saito (Universita' di Kobe) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Global moduli space of stable parabolic connections, Riemann-Hilbert correspondences and geometry of integrable systems 07/07/05 Samuel Boissiere (Università di Mainz) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 McKay correspondences via Hilbert schemes of points on surfaces 30/06/05 Tommaso de Fernex (University of Michigan) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Classi di Chern per varietà algebriche singolari 30/06/05 Renzo Cavalieri (University of Utah) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Geometria enumerativa e teoria di Gromov Witten: contare bitangenti usando mappe stabili 31/05/05 Pedro Luis del Angel (CIMAT, Messico) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Differential equations associated to some algebraic cycles 27/05/05 Carel Faber (KHT, Stoccolma) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Cohomology of moduli spaces of curves related to modular forms 26/05/05 Yuri Zarhin (Penn State University) Aula Chisini, Universita' di Milano, Via C. Saldini, 50 Families of abelian varieties: isogenies and rigidity 19/05/05 Gian Pietro Pirola (Universita' di Pavia) Aula Chisini, Universita' di Milano, Via C. Saldini, 50 Superficie irregolari Lagrangiane 12/05/05 Viacheslav V. Nikulin (University of Liverpool) Aula Chisini, Universita' di Milano, Via C. Saldini, 50 Correspondences of a K3 surface with itself via a general Mukai vector 31/03/05 Fabio Tonoli (Universita' di Bayreuth) Aula C, Universita' di Milano, Via C. Saldini, 50 Superfici sestiche in P^3 con un insieme pari di nodi 24/02/2005 Federica Galluzzi (Universita' degli Studi di Torino) Aula 8, Universita' di Milano, Via C. Saldini, 50 Struttura di Hodge dell'ipersuperficie cubica di P^5 18/02/2005 Paltin Ionescu (Universita' di Bucharest) Sala di rappresentanza del Dipartimento di Matematica dell' Universita' di Milano, Via C. Saldini, 50 Secant defective varieties 17/02/2005 Kieran O'Grady (Universita' di Roma "La Sapienza") Aula 8, Universita' di Milano, Via C. Saldini, 50 4-varieta' simplettiche irriducibili numericamente equivalenti a Hilb2(K3) 17/02/2005 Kieran O'Grady (Universita' di Roma "La Sapienza") Aula 8, Universita' di Milano, Via C. Saldini, 50 Varieta' simplettiche irriducibili (olomorfe) 3/02/05 Alberto Alzati (Universita' degli Studi di Milano) Aula 8, Universita' di Milano, Via C. Saldini, 50 Esistenza e non esistenza di alcune varietà speciali 27/1/05 Roberto Frigerio (Scuola Normale Superiore di Pisa) Aula 9, Universita' di Milano, Via C. Saldini, 50 Varieta' iperboliche con bordo che sono determinate dal loro gruppo fondamentale 20/1/05 Carlo Madonna (Universita' "La Sapienza" di Roma) Aula Chisini, Universita' di Milano, Via C. Saldini, 50 Fibrati vettoriali e schemi di Hilbert di punti su superficie tipo K3 21/12/04 Mark Andrea de Cataldo Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Una discussione su alcune nuove strutture sulla coomologia 16/12/04 Claudio Fontanari (Universita' di Trento) Aula dottorato, Universita' di Milano, Via C. Saldini, 50 Curve su superfici K3 e divisori effettivi su Mg 2/12/04 Marco Franciosi (Universita' di Pisa) Aula Chisini, Universita' di Milano, Via C. Saldini, 50 Immersioni di curve e congettura 1-2-3 18/11/04 Gert Heckman (Università di Nijmegen) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Hypergeometric equations and period maps 11/11/04 Fiammetta Battaglia (Università di Firenze) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Spazi torici associati a politopi non razionali 11/11/04 Luca Migliorini (Universita' di Bologna) Aula Chisini, Universita' di Milano, Via C. Saldini, 50 Strutture algebriche sulla coomologia dello schema di Hilbert di una superficie 07/10/04 Alessandra Sarti (Università di Mainz) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Azioni di gruppo, superfici K3 e reticoli di Picard 22/06/04 Atsushi Noma (Yokohama National University ) Edificio "La Nave" Via Bonardi 9, Milano, Aula interna 3 piano Multisecant lines to projective varieties 07/06/04 Norbert Schappacher (Technische Universitaet Darmstadt) Edificio "La Nave" Via Bonardi 9, Milano, Aula interna 6 piano On various ways of rewriting Italian Algebraic Geometry in the XXth Century 06/05/04 Gilberto Bini (Universita' di Milano) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Sistemi locali sullo spazio dei moduli delle curve iperellittiche 22/04/04 Enrico Carlini (Universita' di Pavia) Edificio "La Nave" Via Bonardi 9, Milano, Aula interna 3 piano Varieta' di somme binarie 15/04/04 Bert van Geemen (Universita’ di Milano) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Il gruppo di Brauer di fibrazioni ellittiche 23/03/04 Cristiano Bocci (Universita’ di Milano) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Una costruzione iterativa di ideali Gorenstein 18/03/04 Luca Chiantini (Universita’ di Siena) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Sulla linearizzazione degli spazi algebrici 04/03/04 Enrique Arrondo (Universidad Complutense de Madrid) Edificio "La Nave" Via Bonardi 9, Milano, Aula interna 3 piano Sottocanonicita' delle sottovarieta' di codimensione due 28/01/04 Antonella Grassi (University of Pennsylvania) Aula dottorato, Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Alcuni invarianti di varieta' di Calabi-Yau di dimensione 3 22/01/04 Gian Pietro Pirola (Universita' di Pavia) Edificio "La Nave" Via Bonardi 9, Milano Aula interna 3 piano Il problema di de Franchis 11/12/03 Enrico Schlesinger (Politecnico di Milano) Aula Chisini, Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Gruppi di Galois di proiezioni 20/11/03 Hisao Yoshihara ( Faculty of Science, Niigata University) Edificio "La Nave" Via Bonardi 9, Milano Aula interna 6 piano Families of Galois closure curves for plane quartic curves 13/11/03 Antonio Laface (Universita' di Milano) Aula Chisini, Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Sistemi lineari su superfici K3 generiche 14/07/03 Gianmario Besana (CP De Paul University, Chicago) Aula C Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Sulla dimensione dello schema di Hilbert di 3-folds speciali 02/07/03 Elham Izadi (University of Georgia, USA) Edificio "La Nave" Via Bonardi 9, Milano Aula interna 3 piano On curves, abelian varieties and the Hodge conjecture 25/06/03 Uwe Nagel (Universita' del Kentucky) Edificio "La Nave" Via Bonardi 9, Milano Aula interna 3 piano Families of degree two curves and certain ropes 24/06/03 Angelo Lopez (Universita' di Roma III) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Sul numero di Eulero di 3-folds di Calbi-Yau e di tipo generale e applicazioni ai quozienti di Chern e ai nodi 15/05/03 Roberto Paoletti (Universita' di Milano Bicocca) Aula Chisini Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Mappe momento e nuclei di Szego equivarianti 13/05/03 Sonia Brivio (Universita' di Pavia) Aula 9 Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Mappa determinante associata a un fibrato di rango 2 09/05/2003 Lucia Caporaso (Università di Roma III) Aula Chisini Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Curve algebriche su campi di funzioni 08/05/2003 Juan Carlos Naranjo (Università di Barcellona) Aula 8 Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Fourier transform and Prym varieties 06/05/2003 Jean-Louis Colliot-Thélène (C.N.R.S e Universita' di Paris Sud) Edificio "La Nave" Via Bonardi 9, Milano Aula interna 6 piano Rationally connected varieties, arithmetic and geometry 30/04/2003 Silvia Benvenuti (Universita' di Pavia) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Un gioco di Lego-Teichmuller 15/04/2003 Fabio Tonoli (Universita di Bayreuth) Aula C Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Insiemi pari di nodi su superfici sestiche: nuovi sviluppi 15/04/2003 Enrico Carlini (Universita di Pavia) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Decomposizione di polinomi e varieta delle secanti 08/04/2003 Flaminio Flamini (Università dell'Aquila) Aula C Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Famiglie di "curve" nodali su 3-folds 01/04/2003 Michele Grassi (Università di Pisa) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Simmetria speculare e varietà autoduali 28/03/2003 Alessandro Ghigi (Università di Pavia) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Geometria kaehleriana sulle varietà di Fano 13/03/2003 Gilberto Bini(Università di Amsterdam) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Alcune osservazioni sulla coomologia dello spazio dei moduli delle mappe stabili 17/02/2003 Roberto Notari (Politecnico di Torino) Edificio "La Nave" Via Bonardi 9, Milano Aula interna 6 piano Costruzione di schemi aritmeticamente Gorenstein 14/01/2003 Lidia Stoppino (Universita' di Pavia) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Sull'articolo: A.Gibney, S Keel, I.Morrison, Towards the ample cone of Mgn 09/01/2003 Alessandro Verra (Universita' di Roma III) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Unirazionalita' di M14 28/11/2002 Davide Franco Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Un teorema sulle superfici sottocanoniche di P^4 21/11/2002 Riccardo Salvati Manni Aula 8, Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Forme modulari e gruppo di Burkhardt 04/11/2002 Cinzia Casagrande (Universita' di Roma, La Sapienza) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Proprieta' combinatoriche delle curve spin stabili 21/10/2002 Irene Sabadini (Politecnico di Milano) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Alcuni risultati sulla connessione dello schema di Hilbert H(d,g) 16/10/2002 Francesco Russo (Universita' di Recife, Brasile) Aula C Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Degenerazioni di proiezioni e applicazioni 11-07-02 Marc Coppens (Katholieke Industriële Hogeschool der Kempen, Geel, Belgium) Edificio "la Nave" Via Bonardi 9, Milano Aula interna 6 piano Very ample linear systems on blowings-up at general points of smooth projective varieties 11-06-02 Arnaud Beauville (Universita' di Nizza) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Algebraic cycles on Jacobian Varieties 28-05-02 Herbert Clemens (University of Utah) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Gradient schemes associated to K-trivial threefolds 09-05-02 Hironori Shiga (CHIBA University, Japan) Edificio "la Nave" Via Bonardi 9, Milano Aula interna 6 piano On certain types of Fuchsian differential equations 09-05-02 Kenji Koike (J. W. Goethe University, Frankfurt) Edificio "la Nave" Via Bonardi 9, Milano Aula interna 6 piano Remarks on the Segre cubic 15-03-02 Elham Izadi (University of Georgia) Edificio "la Nave" Via Bonardi 9, Milano Aula interna 6 piano Deforming curves in Jacobians to non Jacobians 21-02-02 Roberto Pignatelli (Universita' di Beyreuth) Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Aula 7 Fibrazioni di genere piccolo 11-02-02 Roberto Munoz (Universidad Rey Juan Carlos, Madrid) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Projective normality of Enriques surfaces 04-02-02 Massimiliano Mella (Universita' di Ferrara) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Modelli Minimali e Geometria Proiettiva 15/11/2001 Alessio Corti (Universita' di Cambridge) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Grassmanniane pesate e applicazioni 22/11/2001 Giuseppe Pareschi (Universita' di Roma "Tor Vergata") Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Aula C Regolarita' di fasci corerenti su varieta' abeliane 29/11/2001 Ciro Ciliberto (Universita' di Roma "Tor Vergata") Sala di rappresentanza del Dipartimento di Matematicadell'Universita' di Milano, Via C. Saldini, 50 Teoremi di limitatezza per varieta` proiettive 04/10/2001 Gianluca Pacienza Via C. Saldini, 50 Aula C Il cono nef del prodotto simmetrico di una curva generica 12/07/2001 Raquel Mallavibarrena (della Universita' Complutense di Madrid) Sala di rappresentanza del Dipartimento di Matematica dell'Universita' di Milano, Via C. Saldini, 50 Multisecant planes to curves 17/05/2001 Gianluca Occhetta (Universita' di Milano) Edificio "La Nave" Via Bonardi 9 La successione di Eulero-Jaczewski e il problema di Remmert-Van de Ven per varietà toriche 19/04/2001 Silvio Greco (Politecnico di Torino) Edificio "La Nave" Via Bonardi 9 Nodi e nodi apparenti di una curva proiettiva 29/03/2001 Giorgio Ottaviani (Universita' di Firenze) Via C. Saldini, 50 Aula C Sizigie di varieta' toriche 15/03/2001 Gian Pietro Pirola (Universita' di Pavia) Via C. Saldini, 50 Aula C Moduli di superficie irregolari 22/02/2001 Marco Maggesi (Universita' di Milano) Edificio "La Nave" Via Bonardi 9 Coomologia quantistica delle varietà di Fano di dimensione tre. 20/02/2001 Francesco Russo (Universita' di Recife) Via C. Saldini, 50 Aula C Hessiano di una ipersuperficie e varieta' duale 08/02/2001 Francesco Russo (Universita' di Recife) Via C. Saldini, 50 Sizigie Lineari e Geometria Proiettiva 26/01/2001 Silvia Benvenuti (Universita' di Pisa) Via C. Saldini, 50 Complesso di curve e presentazioni finite per il mapping class group 25/01/2001 Marta Rampichini (Universita' di Milano) Via C. Saldini, 50 Algoritmi per il riconoscimento del nodo banale 11/01/2001 Marie-Amelie Bertin (Universita' di Grenoble) Via C. Saldini, 50 On the regularity of varieties having an extremal secant line 14/12/2000 Marco Andreatta Via C. Saldini, 50 Raggi speciali del cono di Mori di una varieta' proiettiva 01/12/2000 Jaroslaw Wisniewski Via C. Saldini, 50 Recent developments in the classification of higher dimensional varieties 12/05/2000 Anthony Geramita (Queen's University e Universita' di Genova) Edificio "La Nave" Via Bonardi 9, Aula interna VII piano Perche' mi interessano i sistemi inversi 13/04/2000 Fabio Tonoli (Universita' di Padova) Via C. Saldini, 50 Aula C Costruzioni e indagini su campi finiti piccoli 06/04/2000 Silvio Greco (Politecnico di Torino) Edificio "La Nave" Via Bonardi 9, Aula interna VII piano Postulazione dei nodi di una curva piana e applicazioni 03/04/2000 Luca Migliorini (Universita' di Trento) Via C. Saldini 50 Introduzione alle categorie derivate 30/03/2000 Gianluca Occhetta (Universita' di Milano) Edificio "La Nave" Via Bonardi 9, Aula interna VII piano Deformazione di curve e fibre di contrazioni estremali 23/03/2000 Giorgio Bolondi (Politecnico di Milano) Edificio "La Nave", Via Bonardi 9, Aula interna del VII piano Discussione sul tema: Genere massimo (e sub-massimale) di curve proiettive 16/03/2000 Mark A. De Cataldo (Universita' di Stony Brook, USA) Via Saldini 50, Aula 9 Hard Lefschetz e la topologia delle mappe algebriche 03/03/2000 Uwe Nagel (Universita' di Paderborn, Germania) Edificio "La Nave", Via Bonardi 9, Aula interna del V piano Some open problems on Gorenstein Liaison