### Seminari

### Prossimi Seminari

- Zero-dimensional symmetry, or locally profinite groups

George Willis, University of Newcastle, Australia

giovedì 21 novembre 2019 alle ore 16:00, Aula U5-3014 (Edificio 5, terzo piano) del Dipartimento di Matematica e Applicazioni dell'Università di Milano-Bicocca, in Via Cozzi 55 - Un viaggio nel mondo dei poliedri

Giuseppe Conti, Università di Firenze

mercoledì 27 novembre 2019 alle ore 15:00, Sala Consiglio - piano 7° - edificio 14 - Propagation of singularities for solutions to Hamilton-Jacobi equations

Piermarco Cannarsa, Università di Roma Tor Vergata

lunedì 2 dicembre 2019 alle ore 15:30, Sala Consiglio del 7 piano, Dipartimento di Matematica, Via Ponzio 31-33, Milano - Come utilizzare le prove invalsi nella pratica d’aula

Alice Lemmo, Università degli studi dell’Aquila

mercoledì 4 dicembre 2019 alle ore 15:00, Sala Consiglio - piano 7° - edificio 14 - Explainability, intepretability and sensitivity analysis

Emanuele Borgonovo, Department of Decision Sciences, BIDSA, Bocconi University, Milano

venerdì 6 dicembre 2019 alle ore 14:30, Aula Saleri - VI piano - The mysteries of L-values

Sarah Zerbes, University College London

martedì 10 dicembre 2019 alle ore 14:00, Sala di Rappresentanza, Dipartimento di Matematica, Via C. Saldini 50 - Translating cardiac models into the clinic

Steven Niederer, Biomedical Engineering, King’s College London

giovedì 12 dicembre 2019 alle ore 14:00, Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO - Long-time asymptotics for evolutionary crystal dislocations models

Matteo Cozzi, University of Bath

martedì 17 dicembre 2019 alle ore 15:30, Aula seminari 3° piano - Nonlinear Peridynamic Models

Giuseppe Maria Coclite, Politecnico di Bari

mercoledì 22 gennaio 2020 alle ore 15:15, Aula seminari 3° piano

### Seminari Passati

- Morphology of the normal and pathological mitral and aortic valves

Antonio Corno, East Midlands Congenital Heart Center, UK.

lunedì 18 febbraio 2019 alle ore 14:00, Aula Seminari 'Saleri' VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano - Edificio 14ABSTRACTThe anatomy of the normal mitral valve and aortic valve will be explained and illustrated in all the specific elements, in order to provide the background required to then understand the mechanism of their opening and closing. The various types of anatomically and functionally bicuspid aortic valve will be then illustrated, with the reasons why the presence of bicuspid aortic valve is frequently associated with malfunctioning of the valve itself and also with diseases of the ascending aorta. Finally, the different mechanism involved in the congenital stenosis and/or regurgitation of the aortic valve will be explained, with the associated consequences on the left ventricular morphology and function.

contact: christian.vergara@polimi.it

- Application of Polyconvexity and multivariable convexity of energy potentials in nonlinear solid mechanics

Javier Bonet, University of Greenwich

giovedì 14 febbraio 2019 alle ore 14:00, Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANOABSTRACTThe presentation will review recent advances in the area of designing and using polyconvex energy potentials to describe the behaviour of solids in the large strain regime in the presence of several physical phenomena such as thermal or electro-mechanical effects. The need for convexity will be justified from the viewpoint of ensuring the existence of real wave speeds in the material at any state of deformation. The convexity of energy potentials with respect to an extended set of variables describing deformation and other multi-physics effects enables the definition of conjugate stresses, thermal and electro-mechanical variables and the formulation of complementary energy functions via the application of the Legendre transforms. In the static case, this leads to the development of a variety of Hu-Washizu or Hellinger-Reissner mixed variation principles that permit the discretisation of different fields with specifically chosen order of accuracy. For instance, in the case of nearly and fully incompressible materials, discretisations that either meet the LBB condition or are appropriately stabilised can be constructed. In the dynamic case, first order conservation laws can be derived for each of the extended set of variables in the energy function. Moreover, convexity enables the definition of a convex entropy-like functional of the primary conserved variables, leading to a symmetrisation of the conservation laws in terms of conjugate stress-like variables and a robust implementation of a Petrov-Galerkin discretisation process. This can be done in a variety of ways, for instance in the case of thermoelasticity two approaches will be discussed, namely, using the Hamiltonian as “entropy-like” convex function or, alternatively, using the so-called “ballistic free energy” as convex entropy extension. Several examples demonstrating the theoretical developments will be provided.

contact: luca.formaggia@polimi.it - Spectral synthesis for systems of exponentials and reproducing kernels

Anton Baranov, Saint Petersburg State University

giovedì 7 febbraio 2019 alle ore 16:00, Sala di Rappresentanza, Dipartimento di Matematica, Via C. Saldini 50, MilanoABSTRACTLet $x_n$ be a complete and minimal system of vectors in a Hilbert space $H$. We say that this system is hereditarily complete or admits spectral synthesis if any vector in $H$ can be approximated by linear combinations of partial sums of the Fourier series with respect to $x_n$. It was a long-standing problem whether any complete and minimal system of exponentials in $L^2(-a,a)$ admits spectral synthesis. Several years ago we gave a negative answer to this question. At the same time we showed that any such system admits the synthesis up to a one- dimensional defect. In the talk we will also discuss related problems for systems of reproducing kernels in Hilbert spaces of entire functions (such as Paley-Wiener, de Branges, Fock). - 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.