Alberto Setti, Università dell ' Insubria, Proprieta stocastiche e spettrali del Laplaciano pesato su varietà Riemanniane. , Monday, May 14, 2012, time 14:00, Aula seminari III piano
Abstract:Abstract:
E noto che lo spettro degli operatori di diffusione e influenzato dalle proprieta stocastiche del corrispondente processo di diffusione. Per esempio, si dimostra facilmente che la ricorrenza del processo di diffusione implica che il bottom dello spettro del corrispondente operatore di diffusione e nullo. Recenti risultatidi Bessa Jorge e Montenegro e di Harmer hanno dato rilevanza ad un interessante legame that la completezza stocastica di certe varieta e lo spettro essenziale del loro Laplaciano. Scopo del seminario e descrivere le possibili relazioni tra completezza stocastica e proprieta spettrali di varieta pesate.

Hélène Frankowska, CNRS and Université Pierre et Marie Curie (Paris 6), Distance Estimates for State Constrained Trajectories of Control Systems, Thursday, April 26, 2012, time 14:45 o'clock, Aula Seminari III piano
Abstract:Abstract:
I will discuss the validity of estimates on the distance of an arbitrary state trajectory of a control system from the set of all state trajectories which lie in a given state constraint set. These estimates have wide-spread application in state constrained optimal control, including justifying the use of the Maximum Principle in normal form and establishing regularity properties of value functions. We focus on linear, $L^{ infty}$ and $W^{1,1}$ distance estimates which, of all the available estimates have, so far, been the most widely used.

Italo Capuzzo Dolcetta, Universita di Roma La Sapienza, New pde s models in optimal control, Friday, April 20, 2012, time 14:00 o'clock, Aula Seminari III piano
Abstract:Abstract:
Nel seminario verranno presentati un introduzione alla teoria dei Mean Field Games di Lasry-Lions e alcuni recenti risultati di approssimazione.

Hao Wu, Fudan University, Shanghai, Well-posedness and long-time behavior of the Hele-Shaw-Cahn-Hilliard system, Friday, April 13, 2012, time 14:00 o'clock, Aula seminari III piano
Abstract:Abstract:
The Hele-Shaw-Cahn-Hilliard model is one of the most popular system describing two-phase flows in porous media or Hele-Shaw cell using the phase-field approach. We will discuss the well-posedness and long-time behavior of the incompressible Hele-Shaw-Cahn-Hilliard system in two and three spatial dimensions. We show the convergence of global weak/strong solution to equilibrium as time goes to infinity with a rate via the Lojasiewicw-Simon technique. Stability of the energy minimizers is also discussed.

Jean Dolbeault, Universite Paris Dauphine, Free energies, nonlinear flows and functional inequalities, Friday, Febraury 17, 2012, time 14:00 o'clock, Aula Seminari III piano
Abstract:Abstract:
This lecture will primarily be devoted to a review of results based on entropy methods in nonlinear diffusion equations. The basic example is the fast diffusion equation in the euclidean space and the study of the asymptotic behaviour of the solutions in self-similar variables. Recent results (in collaboration with G. Toscani) provide interesting refinements for the study of the asymptotic behaviour of the solutions, based on best matching asymptotic profiles rather than on self-similar rescalings. As a consequence, improved Sobolev inequalities have been obtained, thus giving an answer to an old open question raised by H. Brezis and E. Lieb. Nonlocal improvements of standard functional inequalities will also be introduced, based on duality and nonlinear flows approaches. They are connected with mean field models like the Keller-Segel system.

Giovanni Catino, Politecnico di Milano, On the classification of some Einstein-like metrics, Friday, Febraury 03, 2012, time 14:00 o'clock, Aula Seminari III piano
Abstract:Abstract:
In this talk, I will discuss some recent results concerning the classification of some Einstein-like structure, such as Ricci solitons, Yamabe solitons and Einstein solitons. These are special Riemannian manifolds which arise naturally as self similar solutions to some geometric flows and have been studied intensively in recent years.