27 Marzo, 2017 16:30

Lezioni Leonardesche

RANDOM CRACKS IN SPACE

WENDELIN WERNER, ETH Zürich

Aula Chisini, via Saldini 50

abstract

abstract

ABOUT THE SPEAKER: Wendelin Werner is a world renowned scientist, whose exciting work intertwines probability theory with mathematical physics and complex analysis. Werner is often motivated by problems in statistical physics which involve critical phenomena in the large scale behavior of complex multi-particle systems; such as those that arise in phase transitions and percolation. His profound work on stochastic Loewner evolution, the fractal geometry of two dimensional Brownian motion and conformal field theory earned Werner both the Fields medal and the SIAM Pólya Prize (together with collaborators Greg Lawler and Oded Schramm) in 2006. In addition, Werner is the recipient of the European Mathematical Society Prize (2000), the Fermat Prize (2001), the Jacques Herbrand Prize (2003), the Loève Prize (2005) and was inducted into the French Academy of Sciences in 2008. Werner received his Ph.D in 1993 from the Universitè Paris VI under the direction of Jean-François Le Gall and has held positions at the Cambridge University, Universitè Paris-Sud and Ecole Normale Supèrieure before being named Professor of Mathematics at ETH Zürich in 2013.

22 Marzo, 2017 12:15

Seminari di Cultura Matematica

Un gioco cooperativo: lo scambio di donatori di rene

Roberto Lucchetti, Politecnico di Milano

Campus Leonardo, via Bonardi 9, Edificio 14 (Nave), aula B21

ABOUT THE SPEAKER: Wendelin Werner is a world renowned scientist, whose exciting work intertwines probability theory with mathematical physics and complex analysis. Werner is often motivated by problems in statistical physics which involve critical phenomena in the large scale behavior of complex multi-particle systems; such as those that arise in phase transitions and percolation. His profound work on stochastic Loewner evolution, the fractal geometry of two dimensional Brownian motion and conformal field theory earned Werner both the Fields medal and the SIAM Pólya Prize (together with collaborators Greg Lawler and Oded Schramm) in 2006. In addition, Werner is the recipient of the European Mathematical Society Prize (2000), the Fermat Prize (2001), the Jacques Herbrand Prize (2003), the Loève Prize (2005) and was inducted into the French Academy of Sciences in 2008. Werner received his Ph.D in 1993 from the Universitè Paris VI under the direction of Jean-François Le Gall and has held positions at the Cambridge University, Universitè Paris-Sud and Ecole Normale Supèrieure before being named Professor of Mathematics at ETH Zürich in 2013.

20 Marzo, 2017 16:00 in punto

Seminario Matematico e Fisico di Milano

What's in an envelope? Operator theory and numerical ranges

Pamela Gorkin, Bucknell University, Pennsylvania

Sala di rappresentanza, Dipartimento di Matematica, Università degli Studi, Via C. Saldini 50

ABOUT THE SPEAKER: Wendelin Werner is a world renowned scientist, whose exciting work intertwines probability theory with mathematical physics and complex analysis. Werner is often motivated by problems in statistical physics which involve critical phenomena in the large scale behavior of complex multi-particle systems; such as those that arise in phase transitions and percolation. His profound work on stochastic Loewner evolution, the fractal geometry of two dimensional Brownian motion and conformal field theory earned Werner both the Fields medal and the SIAM Pólya Prize (together with collaborators Greg Lawler and Oded Schramm) in 2006. In addition, Werner is the recipient of the European Mathematical Society Prize (2000), the Fermat Prize (2001), the Jacques Herbrand Prize (2003), the Loève Prize (2005) and was inducted into the French Academy of Sciences in 2008. Werner received his Ph.D in 1993 from the Universitè Paris VI under the direction of Jean-François Le Gall and has held positions at the Cambridge University, Universitè Paris-Sud and Ecole Normale Supèrieure before being named Professor of Mathematics at ETH Zürich in 2013.

16 Marzo, 2017 11:00

MOX Seminar

Quasi-optimality of nonconforming methods for linear variational problems

Pietro Zanotti, Universita' degli Studi di Milano

Aula Seminari "Saleri" VI Piano MOX-Dipartimento di Matematica, Edificio 14 POLITECNICO DI MILANO

abstract

abstract

We consider the approximation of linear elliptic variational problems, symmetric for simplicity. According to the Cea’s lemma, conforming Galerkin methods for these problems are quasi-optimal. Conversely, a simple argument reveals that classical nonconforming methods do not enjoy such property. Motivated by this observation, we derive necessary and sufficient conditions for quasi-optimality, within a large class of methods. Moreover, we identify the quasi-optimality constant and discuss its ingredients. In the second part of the talk, we present a detailed construction of two quasi-optimal nonconforming methods for a model problem and show that the corresponding quasi-optimality constants are bounded in terms of the shape parameter of the underlying meshes. This is a joint work with Andreas Veeser.

contact:

paola.antonietti@polimi.it

simona.perotto@polimi.it

16 Marzo, 2017 11:00 in punto

Sezione di Analisi

Nonlinear and Nonlocal Degenerate Diffusions on Bounded Domains

Matteo Bonforte, Universidad Autonoma de Madrid

Aula seminari 3° piano

abstract

abstract

We investigate quantitative properties of nonnegative solutions to a nonlinear fractional diffusion equation, of degenerate type, posed in a bounded domains, with appropriate homogeneous Dirichlet boundary conditions. The diffusion is driven by a quite general class of linear operators that includes the three most common versions of the fractional Laplacian in a bounded domain with zero Dirichlet boundary conditions; many other examples are included. The nonlinearity is assumed to be increasing and is allowed to be degenerate, the prototype being convex powers. We will present some recent results about existence, uniqueness and a priori estimates for a quite large class of very weak solutions, that we call weak dual solutions.
We will devote special attention to the regularity theory: decay and positivity, boundary behavior, Harnack inequalities, interior and boundary regularity, and asymptotic behavior. All this is done in a quantitative way, based on sharp a priori estimates. Although our focus is on the fractional models, our techniques cover also the local case, and provide new results even in this setting.
A surprising instance of this problem is the possible presence of nonmatching powers for the sharp upper and lower boundary behavior. This unexpected phenomenon is a completely new feature of the nonlocal nonlinear structure of this model, and it is not present in the elliptic case.
The above results are contained on a series of recent papers in collaboration with A. Figalli, Y. Sire, X. Ros-Oton and J. L. Vazquez.

15 Marzo, 2017 12:15

Seminari di Cultura Matematica

La matematica dei terremoti.

Alfio Quarteroni, EPFL— Politecnico di Milano (on leave)

Campus Leonardo, via Bonardi 9, Edificio 14 (Nave), aula B21

We investigate quantitative properties of nonnegative solutions to a nonlinear fractional diffusion equation, of degenerate type, posed in a bounded domains, with appropriate homogeneous Dirichlet boundary conditions. The diffusion is driven by a quite general class of linear operators that includes the three most common versions of the fractional Laplacian in a bounded domain with zero Dirichlet boundary conditions; many other examples are included. The nonlinearity is assumed to be increasing and is allowed to be degenerate, the prototype being convex powers. We will present some recent results about existence, uniqueness and a priori estimates for a quite large class of very weak solutions, that we call weak dual solutions.
We will devote special attention to the regularity theory: decay and positivity, boundary behavior, Harnack inequalities, interior and boundary regularity, and asymptotic behavior. All this is done in a quantitative way, based on sharp a priori estimates. Although our focus is on the fractional models, our techniques cover also the local case, and provide new results even in this setting.
A surprising instance of this problem is the possible presence of nonmatching powers for the sharp upper and lower boundary behavior. This unexpected phenomenon is a completely new feature of the nonlocal nonlinear structure of this model, and it is not present in the elliptic case.
The above results are contained on a series of recent papers in collaboration with A. Figalli, Y. Sire, X. Ros-Oton and J. L. Vazquez.

13 Marzo, 2017 11:30 in punto

Sezione di Analisi

Spectra, automata and discrete analogues of the KdV equation

Andrzej Zuk, C.N.R.S. France et Université Paris 7

Aula seminari 6° piano

abstract

abstract

Box-Ball systems are discrete analogues of the KdV equation. We prove that their evolution can be described by automata. With these automata we associate self-adjoint operators. We relate spectral properties of these operators with L^2 Betti numbers of closed manifolds.

9 Marzo, 2017 17:00 in punto

Seminario Matematico e Fisico di Milano

Maximum principle and the principal eigenvalue, a long story

Isabeau Birindelli, Università di Roma La Sapienza

Aula Chisini, Dipartimento di Matematica, Via Saldini 50

abstract

abstract

The link between the principal eigenvalue and the maximum principle has been made very clear since the works of Protter - Weinberger, Pucci and Berestycki-Nirenberg-Varadhan. Its consequences are important and go from regularity of solutions to their very existence.
I will start by giving a survey of this rich field in the classical case of the second order uniformly elliptic operators. Then I will go on describing what and how some of these results extend or not to non linear operators and to degenerate elliptic operators.

8 Marzo, 2017 15:00 in punto

Sezione di Analisi

Null controllability in degenerate and singular parabolic problems

Genni Fragnelli, Università degli Studi di Bari

Aula seminari 6° piano

abstract

abstract

In this talk we will present the problem of null controllability for parabolic systems and we will focus on some recent results for degenerate and singular problems coming from real-world models, such as Biology, Climatology, Medicine.

8 Marzo, 2017 16:15 in punto

Sezione di Analisi

Fractional Hartree equations

Dimitri Mugnai, Università di Perugia

Aula seminari 6° piano

abstract

abstract

We will report on some recent results on fractional Hartree equations having various forms of nonlinearities.