### Seminari

### Prossimi Seminari

**Laser "su misura" per il trattamento di tumori**

Paola Saccomandi, Politecnico di Milano

mercoledì 27 marzo 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Some remarks on the forces exerted by a viscous fluid on a bluff body**

Gianmarco Sperone, Politecnico di Milano

giovedì 28 marzo 2019 alle ore 15:15, Aula seminari 3° piano**Simplicial splines for representation of density functions**

Karel Hron e Jitka Machalova, Palacky University di Olomouc

martedì 2 aprile 2019 alle ore 15:00 precise, Aula Seminari 'Saleri' VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano - Edificio 14**Stima del valore aggiunto di scuola: stato dell'arte del modello INVALSI e prospettive. Quali implicazioni di policy?**

Tommaso Agasisti, Politecnico di Milano

mercoledì 3 aprile 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**On the modelling of particle and pedestrian motion with Fokker-Planck equations**

Alfio Borzì, University of Wuerzburg -Germania-

giovedì 4 aprile 2019 alle ore 14:00, Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Problemi di frontiera libera nelle scienze applicate**

Sandro Salsa, Politecnico di Milano

mercoledì 10 aprile 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Errori sistematici e confondimento degli studi osservazionali basati sui dati dal mondo reale**

Giovanni Corrao, Università degli Studi di Milano-Bicocca

mercoledì 8 maggio 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Inverse Problems in Adaptive Optics**

Ronny Ramlau, RICAM, Austrian Academy of Sciences, Linz, Austria

mercoledì 8 maggio 2019 alle ore 14:00, Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Forma e complessità in Natura: perché il mondo è matematico?**

Pasquale Ciarletta, Politecnico di Milano

mercoledì 15 maggio 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Matematica, società, economia e sviluppo**

Giulia di Nunno, University di Oslo

mercoledì 22 maggio 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Comunicare il progetto. Storytelling e tecniche di rappresentazione**

Francesca Piredda, Politecnico di Milano

mercoledì 29 maggio 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Semi-implicit finite-volume integrators for all-scale atmospheric dynamics**

Piotr Smolarkiewicz, European Centre for Medium-Range Weather Forecasts, Reading, Berkshire, United Kingdom

giovedì 30 maggio 2019 alle ore 14:00, Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

### Seminari Passati

**Poroelasticity: Discretizations and fast solvers based on geometric multigrid methods**

Francisco José Gaspar Lorenz, Department of Applied Mathematics -Zaragoza University - Spain

giovedì 31 gennaio 2019 alle ore 14:00, Sala Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANOABSTRACTThe theory of poroelasticity models the interaction between the deformation and the fluid flow in a fluid-saturated porous medium. Poroelastic models are widely used nowadays in the modeling of many applications in different fields, ranging from geomechanics and petroleum engineer, to biomechanics. The poroelastic equations are often solved in a two-field formulation, where the unknowns are the displacement and the pressure, or in a three-field formulation where the velocity of the fluid is included as a primary variable as well. The numerical solution of these models is usually based on finite element methods. In this talk, we will study some stabilized finite element discretizations for both formulations of the poroelastic problem. Moreover, an important aspect in the numerical simulation of these problems is the efficient solution of the large systems of algebraic equations obtained after discretization. The resulting systems are of saddle point type and we will address their efficient solution by designing suitable geometric multigrid methods.

Contact: luca.formaggia@polimi.it

**Dealing with unreliable computing platforms at extreme scale**

Luc Giraud, INRIA (Inria Bordeaux - Sud-Ouest)

mercoledì 23 gennaio 2019 alle ore 14:00, Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANOABSTRACTThe advent of extreme scale computing platforms will require the use of parallel resources at an unprecedented scale. On the technological side, the continuous shrinking of transistor geometry and the increasing complexity of these devices affect dramatically their sensitivity to natural radiation leading to a high rate of hardware faults, and thus diminish their reliability. Handling fully these faults at the computer system level may have a prohibitive computational and energetic cost. High performance computing applications that aim at exploiting all these resources will thus need to be resilient. In this talk, we will first give an overview of the current trends towards exascale. We will discuss the new challenges to face in terms of platform reliability and associated variety of possible faults. We will then discuss some of the solutions that have been proposed to tackle these errors before discussing in more details some contributions in sparse numerical linear algebra. First, in the context of computing node crashes, we will discuss possible remedies in the framework of linear system or eigenproblem solutions, that are the inner most numerical kernels in many scientific and engineering applications and also ones of the most time consuming parts. Second, we will discuss a somehow more challenging problem related to silent transient soft-errors produced by natural radiation and consisting in a bit-flip in a memory cell producing unexpected results at the application level. In that context we will consider the conjugate gradient (CG) method that is the most widely used iterative scheme for the solution of large sparse systems of linear equations when the matrix is symmetric positive definite. We will investigate through extensive numerical experiments the sensitivity of of CG to bit-flips and further discuss possible numerical criteria to detect the occurrence of such faults.

The above mentioned research activities have been conducted in collaboration with many colleagues including E. Agullo (Inria), S. Cools (University of Antwerpen), E. Fatih-Yetkin (Kadir Has University), P. Salas (CERFACS), W. Vanroose (University of Antwerpen) and M. Zounon (NAG).

contact: luca.bonaventura@polimi.it

**QUANTUM INCOMPATIBILITY WITNESSES**

Alessandro Toigo, Politecnico di Milano

giovedì 17 gennaio 2019 alle ore 11:30 precise, Aula Consiglio VII pianoABSTRACTWe discuss the following variant of the standard minimum error state discrimination problem: Alice picks the state she sends to Bob among one of several disjoint state ensembles, and she communicates him the chosen ensemble only at a later time. Two different scenarios then arise: either Bob is allowed to arrange his measurement set-up after Alice has announced him the chosen ensemble (pre-measurement scenario), or he is forced to perform the measurement before of Alice’s announcement (post-measurement scenario). In the latter case, he can only post-process his measurement outcome when Alice’s extra information becomes available. We demonstrate that quantum incompatibility can always be detected by means of a state discrimination task within the pre-measurement scenario. This is done by showing that only incompatible measurements allow for an efficient use of pre-measurement information in order to improve Bob’s probability of guessing the correct state. The gap between the guessing probabilities with pre- and post-measurement information is thus a witness of the incompatibility of a given collection of measurements. We prove that all linear incompatibility witnesses can be implemented as some state discrimination protocol according to this scheme.**Expected utility maximization beyond the Markovian setting**

Marina Santacroce, Politecnico di Torino

martedì 8 gennaio 2019 alle ore 16:30 precise, Aula Seminari del III pianoABSTRACTAn overview of the recent approaches used to solve

portfolio optimization problems for general market models

is given.

In particular, the focus will be on dynamic programming

techniques and on their applicability to expected utility

maximization in non-Markovian settings for classical

utilities (power, exponential or log type), including the

case of partial information. Moreover, another method

which works for general utilities is presented and

compared to recent results obtained by dynamic

programming.

This talk is based on joint works with M. Mania, R.

Tevzadze and B. Trivellato.

**The Birch-Swinnerton-Dyer conjecture, some recent progress**

Guido Kings, Università di Regensburg

lunedì 7 gennaio 2019 alle ore 16:00, Aula C, Dipartimento di Matematica, Via C. Saldini 50, MilanoABSTRACTFinding rational solutions of polynomial equations is one of the most difficult questions in arithmetic geometry. The Birch-Swinnerton-Dyer conjecture (one of the millennium problems) proposes an answer to this question in the case of elliptic curves. In the last years, using techniques like Euler systems in combination with methods involving p-adic families of modular forms, new insights and results concerning refinements of this conjecture were obtained.

In this talk we want to give an introduction to the Birch-Swinnerton-Dyer conjecture, avoiding all technicalities and review what is known about it. In the end we want to explain the ideas which lead to new results on a refinement of the Birch-Swinnerton-Dyer conjecture.**Advanced polyhedral discretization methods for poromechanical modelling**

Michele Botti , Université de Montpellier

martedì 18 dicembre 2018 alle ore 14:00, Aula Seminari 'Saleri' VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano - Edificio 14ABSTRACTDuring the talk, I will present analytical and numerical results for the (possibly nonlinear) coupled equations of poroelasticity describing the fluid flow in a deformable porous medium. We will focus on novel schemes based on a Hybrid High-Order discretization of the mechanics and a Symmetric Weighted Interior Penalty discontinuous Galerkin discretization of the flow. The method has several assets, including, in particular, the validity in two and three space dimensions, inf-sup stability, and the support of general polyhedral meshes, nonmatching interfaces, and arbitrary space approximation order. Our analysis delivers stability and error estimates that hold also when the constrained specific storage coefficient vanishes, and shows that the constants have only a mild dependence on the heterogeneity of the permeability coefficient. The performance of the method is extensively investigated on a complete panel of model problems using stress-strain laws corresponding to real materials. In the last part of the talk, we will consider the numerical solution of the poroelasticity problem with random physical coefficients in the context of uncertainty quantification. The uncertainty is modelled with a finite set of parameters with prescribed probability distribution. The approximation of the stochastic partial differential system is realized by non-intrusive techniques based on polynomial chaos decompositions. We will conclude by performing a sensitivity analysis to asses the propagation of the input uncertainty on the solutions considering application-oriented test cases.

Contact: paola.antonietti@polimi.it

**Positive solutions to indefinite problems: a topological approach**

Guglielmo Feltrin, Politecnico di Torino

giovedì 6 dicembre 2018 alle ore 15:30, Aula seminari 3° pianoABSTRACTIn this seminar, we present some recent existence and multiplicity results for positive solutions of boundary value problems associated with second-order nonlinear indefinite differential equations. More precisely, we deal with the ordinary differential equation

u?? + a(t)g(u) = 0,

where a: [0,T] ? R is a Lebesgue integrable sign-changing weight and g: [0,+?[ ? [0,+?[ is a continuous nonlinearity.

We focus on the periodic boundary value problem and on functions g(u) with superlinear growth at zero and at infinity (including the classical superlinear case g(u) = up, with p > 1). Exploiting a new approach based on topological degree theory, we show that there exist 2m ? 1 positive solutions when a(t) has m positive humps separated by negative ones and the negative part of a(t) is sufficiently large. In this manner, we give a complete answer to a question raised by Butler (JDE, 1976) and we solve a conjecture by G ?omez-Ren ?asco and L ?opez-G ?omez (JDE, 2000). The method also applies to Neumann and Dirichlet boundary conditions and, furthermore, provides a topological approach to detect infinitely many subharmonic solutions and globally defined positive solutions with chaotic behaviour.

Thereafter, we illustrate other directions for the research on indefinite problems: super-sublinear problems, models in population genetics, and also problems involving more general differential oper- ators, as the Minkowski-curvature one or the one-dimensional p-Laplacian. Exact multiplicity results and indefinite problems in the PDE setting are also discussed.

The talk is based on joint works with Alberto Boscaggin (University of Torino), Elisa Sovrano (University of Porto) and Fabio Zanolin (University of Udine) and on the book “Positive Solutions to Indefinite Problems. A Topological Approach” (Frontiers in Mathematics, Birkh ?auser/Springer, 2018).**A decomposition of the Hilbert scheme given by Gröbner schemes**

Yuta Kambe, Saitama University

mercoledì 5 dicembre 2018 alle ore 11:00 precise, Aula seminari III pianoABSTRACTWe 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.