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

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  • 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
  • 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
    ABSTRACT
    The image quality of ground based astronomical telescopes suffers from turbulences in the atmosphere. Adaptive Optics (AO) systems use wavefront sensor measurements of incoming light from guide stars to determine an optimal shape of deformable mirrors (DM) such that the image of the scientific object is corrected after reflection on the DM(s). The operation of the AO systems of the new generation of large astronomical telescopes under construction requires new mathematical methods that achieve reconstruction in real time. In the talk we will in particular focus on methods for wavefront reconstruction from pyramid sensor data and an analysis of the atmospheric tomography operator.

    Contact christian.vergara@polimi.it
  • Regularity for the p-Laplace equation and system in minimally regular domains
    Andrea Cianchi, Università di Firenze
    mercoledì 8 maggio 2019 alle ore 16:00, Aula Seminari del 6 piano, Edificio La Nave, Via Ponzio 32-34
    ABSTRACT
    Some aspects of the global regularity of solutions to boundary value problems for nonlinear elliptic equations and systems of p-Laplacian type will be discussed. In particular, second-order regularity properties of solutions, and the boundedness of their gradient will be focused. The results to be presented are optimal as far as the regularity of the right-hand sides of the equations and of the boundary of the ground domains are concerned. The talk is based on joint researches with V.Maz'ya.
  • Financial stability and macroprudential policy
    Stefano Borgioli, European Central Bank
    martedì 7 maggio 2019 alle ore 17:00, Aula seminari del sesto piano
    ABSTRACT
    Financial stability can be defined as a condition in which the financial system – which comprises financial intermediaries, markets and market infrastructures – is capable of withstanding shocks and the unravelling of financial imbalances. In the seminar we discuss some financial stability analysis tools and the implications on macroprudential policy at ECB.
  • Mirror symmetry and smoothing toric Fano 3-folds
    Alessio Corti, Imperial College Londra
    lunedì 6 maggio 2019 alle ore 14:00, Sala di Rappresentanza, Dipartimento di Matematica, Via C. Saldini 50, Milano
    ABSTRACT
    I describe some conjectures on smoothing toric Fano 3-folds
    motivated by mirror symmetry.
  • Markovian Extensions of Symmetric Second Order Elliptic Differential Operators
    Andrea Posilicano, Università degli Studi dell'Insubria
    martedì 30 aprile 2019 alle ore 15:15, Aula seminari 3° piano
    ABSTRACT
    We give a complete classification of the Markovian self-adjoint extensions of the minimal realization of a second order elliptic differential operator on a bounded n-dimensional domain by providing an explicit one-to-one correspondence between such extensions and the class of Dirichlet forms on the boundary which are additively decomposable by the bilinear form of the Dirichlet-to-Neumann operator plus a Markovian form. By such a result two further equivalent classifications are provided: the first one is expressed in terms of a decomposition of the bilinear forms associated to the extensions, the second one uses the decomposition of the resolvents provided by the Krein formula. The Markovian part of the decomposition allows to characterize the operator domain of the corresponding extension in terms of Wentzell-type boundary conditions. Some analogous results hold also in a nonlinear setting.
  • Limit Theorems for the Fractional Non-homogeneous Poisson Process
    Enrico Scalas, University of Sussex
    martedì 16 aprile 2019 alle ore 14:30, Aula seminari del sesto piano
    ABSTRACT
    The fractional non-homogeneous Poisson process was introduced by a time-change of the non-homogeneous Poisson process with the inverse ?-stable subordinator. We propose a similar definition for the (non-homogeneous) fractional compound Poisson process. We give both finite-dimensional and functional limit theorems for the fractional non-homogeneous Poisson process and the fractional compound Poisson process. The results are derived by using martingale methods, regular variation properties and Anscombe's theorem. Eventually, some of the limit results are verified in a Monte Carlo simulation.

    This is a joint work with Nikolai Leonenko and Mailan Trinh.