SEMINARI DI MATEMATICA
Giovedì 18 ottobre 2018
*Scuola Normale Superiore*
Pisa
Sala Conferenze, Collegio Puteano
si terranno i seguenti seminari:
14:30 *Paolo Buttà* ( Università di Roma "La Sapienza"),
*“On the large deviations of interface motions in statistical mechanics
models”*
*Abstract:*
*In this talk, I consider the sharp interface limit of the action
functional associated to either the Glauber dynamics for Ising systems with
Kac potentials or the Glauber+Kawasaki process. The corresponding limit
functionals provide, in the sense of large deviations theory, the
probability of deviations from the mean curvature flow. I discuss, in the
case of smooth interfaces, the derivation of these functionals, for which
explicit formulae of the mobility and transport coefficients are given.
This is joint work with L. Bertini and A. Pisante.*
15:20 *Michela Ottobre* (Heriot-Watt University, Edimburgh),
*“Beyond the Hoermander condition”*
*Abstract:*
*The study of diffusion processes of elliptic and hypoelliptic type has by
now produced a fully-fledged theory, involving several branches of
mathematics: stochastic analysis, analysis of differential operators,
(sub-)Riemannian geometry and control theory, just to mention the main
players. One of the key steps in the development of such a theory has been
the seminal paper of Hoermander and a large body of work has been dedicated
for over 40 years to the study of diffusion processes under the Hoermander
Condition (HC), which is a sufficient condition for hypoellipticity. We
propose to study processes that do not, in general, satisfy the HC. In
place of the HC, we wish to enforce a weaker condition, the so-called UFG
condition, introduced by Kusuoka and Strook with probabilistic motivations,
and, independently, by Sussman, Hermann and Lobry, this time in the field
of control theory. In particular, Kusuoka and Strook showed that it is
still possible to build a solid PDE theory for diffusion semigroups even in
absence of the Hoermander condition. We will present new results on the
geometry and long time behaviour of diffusion semigroups that do not
satisfy the Hoermander condition. Our interest in UFG diffusions stems from
the observation that they constitute a large class of SDEs which exhibit
multiple invariant measures and such that it is possible to determine in a
systematic way the basin of attraction of each equilibrium state. This is
a joint work with P. Dobson (Maxwell Institute), T. Cass and D. Crisan
(Imperial College).*
16:10 *Boguslaw Zegarlinski* (Imperial College London),
*“Hypoelliptic diffusion in noncommutative setup”*
*Abstract:*
*I will review results and problems concerning hypoelliptic diffusion and
coercive (Poincare and Log-Sobolev) inequalities.*
Tutti gli interessati sono invitati a partecipare.
Classe di Scienze
Valeria Giuliani
Scuola Normale Superiore
Servizio alla Didattica e Allievi
tel. 050 509260
Piazza dei Cavalieri, 7
56126 Pisa
E-mail: valeria.giuliani(a)sns.it
E-mail: classi(a)sns.it