Direttore Vicario: Prof. Gabriele Grillo
Responsabile Gestionale: Dr.ssa Franca Di Censo


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Prossimi Seminari

  • Working with compositional data in coordinates
    Eva Fiserova, Palacky University Olomouc, Czech Republic
    mercoledì 21 novembre 2018 alle ore 14:30, aula Saleri VI piano
  • Illuminazione, visione e opere d’arte: il punto di vista del fisico
    Farini Alessandro, Istituto Nazionale di Ottica, CNR, Firenze
    mercoledì 21 novembre 2018 alle ore 15:00, Sala Consiglio VII piano
  • An overview of some mathematical and computational problems in Network Science
    Michele Benzi, Scuola Normale Superiore, Pisa
    giovedì 22 novembre 2018 alle ore 14:00,  Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
    Shigefumi Mori, Kyoto University Institute of Advanced Study
    lunedì 26 novembre 2018 alle ore 16:30, Aula Chisini, Diparimento di Matematica, Via C. Saldini 50
  • The Quantitative Alexandrov Theorem in Space forms
    Luigi Vezzoni, Università degli Studi di Torino
    martedì 27 novembre 2018 alle ore 15:15, Aula seminari 3° piano
  • First Principles Determination of Reaction Rates
    Carlo Cavallotti, Dipartimento di Chimica, Materiali e Ingegneria Chimica, “G. Natta”, Politecnico di Milano
    martedì 27 novembre 2018 alle ore 10:30, aula Saleri VI piano
  • Emodinamica della circolazione epatica: problemi e nuove acquisizioni
    Massimiliano Tuveri, Azienda Ospedaliera Universitaria Integrata, Verona, Italy
    giovedì 29 novembre 2018 alle ore 11:30, aula consiglio VII piano
  • Characterization of Attraction Domains for Generic Quantum Semigroups
    Damiano Poletti, Politecnico di Milano
    giovedì 29 novembre 2018 alle ore 14:30 precise, Aula Seminari III piano

Seminari Passati

  • A representation formula for the Laplacian of the distance function
    Andrea Mondino, University of Warwick
    mercoledì 21 marzo 2018 alle ore 15:15, Sala del Consiglio 7° piano
    In the seminar I will present a recent work in collaboration with Fabio Cavalletti (SISSA) where, using techniques from optimal transportation, we prove a rather explicit representation formula for the Laplacian of the distance function in spaces with Ricci curvature bounded below. Even if the paper deals with rather general non-smooth spaces, since some results seem new even for smooth manifolds, the seminar will be mostly focused on the smooth framework.
  • Collisions and chaos in the Boltzmann-Grad limit
    Sergio Simonella, ENS Lione
    mercoledì 21 marzo 2018 alle ore 14:45 precise, Aula seminari MOX, VI piano
    I will review our current state of knowledge on the mathematical derivation of the Boltzmann equation from Newtonian systems. This problem has been the objective of intensive effort over recent years. I will focus on the size of correlations in the dilute gas and discuss some delicate aspects of the convergence in the kinetic limit. A statistical analysis of collisions via analytical tools provides new insights on the scale transition.
  • “The Quantization approach for estimating Exposures in Counterparty risk. Review with numerical Applications”
    martedì 20 marzo 2018 alle ore 12:15, Aula Seminari Sesto Piano
  • Isogeometric-analysis-based Multi-Index Stochastic Collocation for Elliptic PDEs with random data
    Lorenzo Tamellini, Istituto “E. Magenes”, Consiglio Nazionale delle Ricerche, Pavia
    martedì 20 marzo 2018 alle ore 11:00, Aula Seminari ‘Saleri’ VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano – Edificio 14
    In many engineering applications governed by PDEs, the parameters of the equations (coefficients, forcing terms, boundary and initial conditions, shape of the domain) are not known exactly but rather affected by a certain degree of uncertainties, and can be described by means of random variables (or random fields).

    Uncertainty Quantification (UQ) aims at estimating how the randomness of these “input” parameters affects the “outputs” of the PDE, typically its solution or functionals thereof. UQ techniques are often based on repeatedly solving the PDE at hand for different combinations of the input parameters (i.e., a sampling approach), which requires a significant computational effort.
    To reduce such effort, so-called “multi-level” and “multi-index” methods have recently been proposed. These methods explore the variability of the PDE outputs using a hierarchy of suitably chosen discretization levels to balance the PDE discretization error and the sampling error, and refine the discretization of the PDE only when needed. We emphasize in particular that these methodologies are completely “black-box”, in the sense that they allow reuse of legacy PDE solvers, and are moreover
    embarrassingly parallel.

    In this talk we describe in detail one such method, i.e., the so-called Multi-Index Stochastic Collocation method (MISC), which is closely related to the quite popular Sparse-Grids Stochastic Collocation method for the approximation of PDE with random data.
    In particular, this method relies on PDE solvers with tensor structure. To this end, we use Isogeometric Analysis (IGA), which is a technique introduced in the early 2000 to bridge the gap between Computer Aided Design (CAD) and PDE-based engineering analysis.
    The core idea of IGA is to use the basis functions used by CAD designers to describe geometries (typically Cubic Splines or Non-Uniform Rational B-Splines) as a basis for the approximation of the solution of the PDE as well; the PDE is then solved a traditional Galerkin approach.
    Beside the fact that its tensorized construction makes IGA very suitable in the MISC framework, attractive features of IGA are the simplified treatment of complex geometries, and the fact that basis functions with high-order and high-degree of regularity can be easily generated, thanks to the flexibility of the splines bases.

    This is a joint work with Joakim Beck and Raul Tempone (KAUST), Abdul-Lateef Haji-Ali (Oxford) and Fabio Nobile (EPFL).


  • One-Slice Preserving Functions of a Quaternionic Variable
    Chiara de Fabritiis, Università Politecnica delle Marche
    giovedì 15 marzo 2018 alle ore 14:00 precise, Aula seminari del terzo piano
    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)
  • The constant scalar curvature equation in some singular spaces
    Gilles Carron, Laboratoire de Mathématiques Jean Leray (UMR 6629), Université de Nantes, CNRS
    mercoledì 14 marzo 2018 alle ore 16:30, Sala Consiglio, 7 piano, Edificio La Nave, Via Bonardi 9
    I will survey the recent results about the Yamabe problem on stratified spaces. I will first introduce the scalar curvature and the Yamabe equation for the constant scalar curvature equation and its variational formulation and the results of Obata, Trudinger, Aubin and Schoen for smooth compact manifold. Then I will describe the geometry of stratified space with some 2D and 3D examples. Eventually I will formulate the Yamabe problem for stratified space and explained some of the recent results and will explain some perspectives.
  • Spectral distribution of sequences of structured matrices: GLT theory and applications
    Debora Sesana, University of Insubria – Como –
    martedì 13 marzo 2018 alle ore 15:00, Aula Seminari ‘Saleri’ VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano – Edificio 14
    Any discretization of a given differential problem for some sequence of stepsizes h tending to zero leads to a sequence of systems of linear equations {Am xm = bm}, where the dimension of {Am} depends on h and tends to infinity for h going to 0. To properly face the solution of such linear systems, it is important to deeply understand the spectral properties of the matrices {Am} in order to construct efficient preconditioners and to study the convergence of applied iterative methods. The spectral distribution of a sequence of matrices is a fundamental concept. Roughly speak- ing, saying that the sequence of matrices {Am} is distributed as the function f means that the eigenvalues of Am behave as a sampling of f over an equispaced grid of the domain of f, at least if f is smooth enough. The function f is called the symbol of the sequence. Many distribution results are known for particular sequences of structured matrices: diagonal matrices, Toeplitz matrices, etc. and an approximation theory for sequences of matrices has been developed to deduce spectral distributions of “complicated” matrix sequences from the spectral distribution of “simpler” matrix sequences. In this respect, recently, has played a fundamental role the theory of Generalized Locally Toeplitz (GLT) sequences (introduced by Tilli (1998) and Serra-Capizzano (2002, 2006)), which allows to deduce the spectral properties of matrix sequences obtained as a combination (linear combinations, products, inversion) of Toeplitz matrices and diagonal matrices; to this category belong many stiffness matrices arising from the discretization, using various methods, of PDEs. We present the main concepts of this theory with some applications.
    This is a joint work with Stefano Serra-Capizzano and Carlo Garoni.

    [1] C. Garoni, C. Manni, S. Serra-Capizzano, D. Sesana, H. Speleers. Spectral analysis and spectral symbol of matrices in isogeometric Galerkin methods. Mathematics of Computation 85 (2016), pp. 1639–1680.
    [2] C. Garoni, C. Manni, S. Serra-Capizzano, D. Sesana, H. Speleers. Lusin theorem, GLT sequences and matrix computations: an application to the spectral analysis of PDE discretization matrices. Journal of Mathematical Analysis and Applications, 446 (2017), pp. 365–382.
    [3] C. Garoni, S. Serra-Capizzano. Generalized Locally Toeplitz Sequences: Theory and Applications. Springer 2017.
    [4] C. Garoni, S. Serra-Capizzano, D. Sesana. Block Locally Toeplitz Sequences: Construction and Properties. Springer INdAM Series: proceeding volume of the Cortona 2017 meeting, submitted.
    [5] C. Garoni, S. Serra-Capizzano, D. Sesana. Block Generalized Locally Toeplitz Sequences:
    Topological Construction, Spectral Distribution Results, and Star-Algebra Structure.
    Springer INdAM Series: proceeding volume of the Cortona 2017 meeting, submitted.


  • Post-Quantum Group-based Cryptography
    Delaram Kahrobaei, New York City College of Technology
    giovedì 8 marzo 2018 alle ore 14:30 precise, Aula seminari, III piano, Dipartimento di matematica
    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.