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

 Seminari

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Prossimi Seminari

  • A mathematical-physics approach to machine learning
    Pierluigi Contucci, Dipartimento di Matematica Università di Bologna
    giovedì 30 gennaio 2020 alle ore 14:00, Aula Saleri VI piano
  • Modeling and simulation of thermo-poroelastic processes in fractured geothermal reservoirs
    Eirik Keilegavlen, Department of Mathematics, University of Bergen, Norway
    giovedì 20 febbraio 2020 alle ore 11:30, Aula Saleri - VI piano

Seminari Passati

  • Multiple solutions for the 2-dimensional Euler equations
    Alberto Bressan,  Pennsylvania State University
    lunedì 27 maggio 2019 alle ore 16:00 precise, Aula U5-3014 (Edificio 5 terzo piano), Dip. Matematica e Applicazioni, Via Cozzi 55, Milano
    ABSTRACT
    In one space dimension, it is well known that hyperbolic conservation
    laws have unique entropy-admissible solutions, depending continuously on
    the initial data. Moreover, these solutions can be obtained as limits of
    vanishing viscosity approximations.

    For many years it was expected that similar results would hold in
    several space dimensions. However, fundamental work by De Lellis,
    Szekelyhidi, and other authors, has shown that multidimensional
    hyperbolic Cauchy problems usually have infinitely many weak solutions.
    Moreover, all known entropy criteria fail to select a single admissible one.

    In the first part of this talk I shall outline this approach based on a
    Baire category argument, yielding the existence of infinitely many weak
    solutions.

    I then wish to discuss an alternative research program,
    aimed at constructing multiple solutions to some specific Cauchy
    problems. Starting with some numerical simulations, here the eventual
    goal is to achieve rigorous, computer-aided proofs of the existence of
    two distinct self-similar solutions with the same initial data.
    While solutions obtained via Baire category have turbulent nature, these
    self-similar solutions are smooth, with the exception of one or two
    points of singularity. They are thus much easier to visualize and
    understand.
  • 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
  • Mathematical Models of Markovian Dephasing
    Franco Fagnola, Politecnico di Milano
    venerdì 17 maggio 2019 alle ore 11:30 precise, Aula Seminari III piano
    ABSTRACT
    We develop a notion of dephasing under the action of a quantum? Markov semigroup in terms of convergence of operators to a block-diagonal? form determined by irreducible invariant subspaces. If the latter are all ?one-dimensional, we say the dephasing is maximal. We study characterization ?of a maximally dephasing evolution in terms of unitary dilations ?with only classical noise. In particular, we introduce an intrinsic? quantity constructed from the generator which quantities the? degree of obstruction to having a classical diffusive noise model.? (Joint work with J.E. Gough, H.I. Nurdin and L. Viola)?
  • 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
  • How to hear the shape of a drum
    Fabio Cipriani, Politecnico di Milano
    martedì 14 maggio 2019 alle ore 15:30, Aula seminari 3° piano
    ABSTRACT
    In a iconic 1912 paper Hermann Weyl, motivated by problems posed by the physicist H.A. Lorentz about J.H. Jeans's radiation theory, showed that the dimension and the volume of a Euclidean domain may be traced from the asymptotic distribution of the eigenvalues of its Laplace operator.
    In a as much famous 1966 paper titled "Can one hear the shape of a drum" Marc Kac popularized this and related problems connecting geometry and spectrum. He noticed that the hope to characterize {\it isometrically}, Euclidean domains or compact Riemannian manifolds by the spectrum of the Laplace operator, is vain: John Milnor in 1964 had showed the existence of non isometric 16 dimensional tori sharing a common (discrete) spectrum.

    The aim of the talk is to show how to recognize {\it conformal maps} between Euclidean domains as those homeomorphisms which transform multipliers of the Sobolev-Dirichlet spaces of a domain into multipliers of the other and leave invariant the {\it fundamental tone} or {\it first nonzero eigenvalue} of the Dirichlet integral with respect to the energy measures of any multiplier. Related results hold true for {\it quasiconformal and bounded distortion maps}.
    In the opposite direction, we prove that the trace of the Dirichlet integral, with respect to the energy measure of a multiplier, is a Dirichlet space that only depends upon the orbit
    of the conformal group of the Euclidean space on the multiplier algebra.

    The methods involve potential theory of Dirichlet forms (changing of speed measure, multipliers) and the Li-Yau conformal volume of Riemannian manifolds.

    This is a collaboration with Jean-Luc Sauvageot C.N.R.S. France et Universit\'e Paris 7.
  • Soluzioni a valori misure di equazioni di evoluzione nonlineari
    Alberto Tesei, Università degli Studi di Roma "La Sapienza"
    martedì 14 maggio 2019 alle ore 14:30, Aula seminari 3° piano
    ABSTRACT
    Soluzioni a valori misure si presentano in modo naturale per importanti classi di equazioni di evoluzione nonlineari (equazione dei mezzi porosi, equazioni "forward-backward", leggi di conservazione). Nel seminario saranno esposti alcuni recenti risultati di esistenza, unicità e comportamento qualitativo di soluzioni entropiche
    a valori misure di Radon di leggi di conservazione iperboliche in una dimensione spaziale, con flusso limitato e lipschitziano. Tempo permettendo, sarà discusso il legame fra tali soluzioni e soluzioni viscose discontinue di equazioni di Hamilton-Jacobi. I risultati presentati sono contenuti in alcuni lavori con M. Bertsch, F. Smarrazzo e A. Terracina.
  • Modelli matematici degli aggregati cellulari: Batteri, protisti, cellule staminali
    Roberto Natalini, Istituto per le Applicazioni del Calcolo - CNR - Roma
    lunedì 13 maggio 2019 alle ore 16:00, Sala di Rappresentanza, Dipartimento di Matematica, Via C. Saldini 50, Milano
    ABSTRACT
    Da qualche anno a questa parte nel mondo matematico sono in corso molte ricerche
    per cercare di descrivere in modo soddisfacente e predittivo il comportamento
    di aggregati cellulari a vari livelli di evoluzione e organizzazione.
    Questi modelli possono aiutare biologi e medici a validare meglio la loro ricerca,
    esplorando ipotesi ed alternative altrimenti impraticabili.
    In questo seminario esporrò alcuni risultati che ho ottenuto negli ultimi anni su alcuni di questi problemi: crescita di biofilm, movimento di protisti su reti, morfogenesi.
    I modelli matematici sono tutti di tipo differenziale e hanno in comune il movimento a velocità finita delle cellule, pur in contesti matematici abbastanza diversi.
  • Deep Learning, Finite Element and Multigrid Methods
    Jinchao Xu, CCMA, Pennsylvania State University
    giovedì 9 maggio 2019 alle ore 14:00, Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
    ABSTRACT
    In this talk, I will first discuss relationship between some deep learning models and traditional algorithms such as finite element and multigrid methods. Such relationships can be used to study, explain and improve the model structures, mathematical properties and relevant training algorithms for deep neural networks. I will report a class of new training algorithms that can be used to improve the efficiency of convolutional neural networks (CNN) by significantly reducing the redundancy of the model without losing accuracy. By combining multigrid and deep learning methodologies, I will present a unified model, known as MgNet, that simultaneously recovers some CNNs for image classification and multigrid methods for solving discretized PDEs. MgNet can also be used to derive a new class of CNNs that mathematically unify many existing CNN models and practically prove to be computationally competitive.

    Contact: alfio.quarteroni@polimi.it