|16/05/18||Seminario||16:00||17:00||1201 Dal Passo||Jacopo Bassi||SISSA||C*-algebras associated to horocycle flows
Murray and von Neumann introduced the notion of crossed product to give examples of different types of factors. Since then many von Neumann algebras and C*-algebras with interesting properties have been constructed following this pattern. We will give an example of a class of C*-algebras to which the classification result by Elliott, Gong, Lin and Niu of 2015 cannot be applied and see some of their properties.
|15/05/18||Seminario||14:30||15:30||1201 Dal Passo||Philippe Souplet||Université Paris XIII||Reaction-diffusion systems with dissipation of mass: old and new results.
We consider positivity-preserving reaction-diffusion systems of the form
$$partial_t u_i-d_iDelta d_i=f_i(u),qquad u=(u_1,dots,u_m),$$
under the Neumann boundary conditions, with the structure condition $sum f_ile 0$, which guarantees that the total mass is nonincreasing in time.
Such systems are often encountered in applications, for instance in models of reversible chemistry.
Whereas global existence and boundedness of solutions is easy in the equidiffusive case $d_iequiv d$,
the question becomes quite involved in the case when the $d_i>0$ are different
(a case which is indeed relevant in models of chemical reactions),
and there has been an abundant mathematical literature on this question in the past 30 years.
Various sufficient conditions on the nonlinearities $f_i$ for global existence are known, as well as examples of finite time blow-up for certain systems. The latter is a special case of the so-called diffusion induced blow-up phenomenon.
We will discuss old and new results on this subject.
|08/05/18||Seminario||14:30||15:30||1201 Dal Passo||Adriano Pisante||Sapienza, Università di Roma||Large deviations for the stochastic Allen-Cahn approximation of the mean curvature flow|
We consider the sharp interface limit for the Allen-Cahn equation on the three dimensional torus with deterministic initial condition and deterministic or stochastic forcing terms. In the deterministic case, we discuss the convergence of solutions to the mean curvature flow, possibly with a forcing term, in the spirit of the pioneering work of Tom Ilmanen (JDG '93). In addition we analyze the convergence of the corresponding action functionals to a limiting functional described in terms of varifolds. In the second part I will comment on related results for the stochastic case, describing how this limiting functional enters in the large deviation asymptotics for the laws of the corresponding processes in the joint sharp interface and small noise limit.
|24/04/18||Seminario||14:30||15:30||1201 Dal Passo||Fabio Camilli||Sapienza, Università di Roma||Time-fractional Mean Field Games|
We consider a Mean Field Games model where the dynamics of the agents is subdiffusive. According to the optimal control
interpretation of the problem, we get a
system involving Hamilton-Jacobi-Bellman and Fokker-Planck equations with time-fractional derivatives.
We first discuss separately the well-posedness of each of the two equations and
then of the Mean Field Games system.
|19/04/18||Colloquium||15:30||16:30||1201 Dal Passo||Maciej ZWORSKI||Berkeley||From classical to quantum and back
Microlocal analysis exploits mathematical manifestations of the classical/quantum (particle/wave) correspondence and has been a very successful tool in spectral theory and partial differential equations. We can say that these two fields lie on the "quantum/wave side".
In the last few years microlocal methods have been applied to the study of classical dynamical problems, in particular of chaotic flows. That followed the introduction of specially tailored spaces by Blank--Keller--Liverani, Baladi--Tsujii and other dynamicists and their microlocal interpretation by Faure--Sjoestrand.
I will explain how it works in the context of Ruelle resonances, decay of correlations and meromorphy of dynamical zeta functions and will also present some recent advances by Dyatlov--Guillarmou, Dang--Riviere and Hadfield.
The talk will be non-technical and is intended as an introduction to both microlocal analysis and to chaotic dynamics.
|17/04/18||Seminario||15:00||16:00||1201 Dal Passo||Marco Mazzola||Univ. Pierre et Marie Curie (Paris VI)||Necessary optimality conditions for infinite dimensional state constrained control problems
We consider semilinear control systems in infinite dimensional Banach spaces, in the presence of constraints for the state of the system. Necessary optimality conditions for a Mayer problem associated to such systems will be discussed. In particular, a simple proof of a version of the constrained Pontryagin maximum principle, relying on infinite dimensional neighbouring feasible trajectories results, will be provided. This proof includes sufficient conditions for the normality of the maximum principle. Some applications to control problems governed by PDEs will be discussed. This talk is based on a joint work with Hélène Frankowska and Elsa Maria Marchini.
|13/04/18||Seminario||16:00||17:00||1101 D'Antoni||René SCHOOF||Università di Roma "Tor Vergata"||Il teorema di Lagrange per schemi in gruppi piatti e finiti
Il teorema di Lagrange dice che in un gruppo di cardinalità n la potenza n-esima di ogni elemento è uguale all’elemento neutro. Una congettura classica afferma che un risultato simile vale per schemi in gruppi piatti e finiti. Spiegherò la dimostrazione di un caso speciale della congettura.
|13/04/18||Seminario||14:30||15:30||1101 D'Antoni||Velleda BALDONI||Università di Roma ||Multiplicities & Kronecker coefficients
Multiplicities of representations appear naturally in different contexts and as such their description could use different languages. The computation of Kronecker coefficients is in particular a very interesting problem which has many
I will describe an approach based on methods from symplectic geometry and residue calculus (joint work with M. Vergne and M. Walter). I will state the general formula for computing Kronecker coefficients and then give many examples computed using an algorithm that implements the formula.
The algorithm does not only compute individual Kronecker coefficients, but also symbolic formulas that are valid on an entire polyhedral chamber. As a byproduct, it is possible to compute several Hilbert series.
|10/04/18||Seminario||14:30||15:30||1201 Dal Passo||Massimo Grossi||Universita' di Roma "La Sapienza"||Radial nodal solution for Moser-Trudinger problems|
We study the asymptotic behavior of least-energy nodal solutions for suitable Moser-Trudinger problems. We will show that appear different phenomena with respect to other nonlinearities (for example power or sinh-type nonlinearites).
|27/03/18||Seminario||14:30||15:30||1201 Dal Passo||Alessio Pomponio||Politecnico di Bari||The Born-Infeld equation: solutions and equilibrium measures|
In this talk, we deal with the Born-Infeld equation which appears in the Born-Infeld nonlinear electromagnetic theory.
In the first part of the talk, we discuss existence, uniqueness and regularity of the solution of the Born-Infeld equation. In the second part, instead, we study existence of equilibrium measures, namely distributions that produce least-energy potentials among all the possible charge distributions, and properties of the corresponding equilibrium potentials.
The results have been obtained in joint works with Denis Bonheure, Pietro d'Avenia and Wolfgang Reichel.