Announcement of two talks in the probability seminar at the University of Pisa.

DATE AND TIME: Tuesday, June 27, 11:00h - 13:00h

LOCATION: Aula Seminari, Dipartimento di Matematica, Universita' di Pisa

SPEAKER 1: Remi Catellier (Université de Nice Sophia-Antipolis)

TITLE: Averaging along irregular curves and regularization of ODEs.

ABSTRACT: Paths of some stochasic processes such as fractional Brownian Motion have some amazing regularization properties. It is well known that in order to have uniqueness in differential systems such as $dy_t = b(y_t) dt$, $b$ needs to be quite regular. However, the oscillations of a stochastic process added to the system will guarantee uniquneness for really irregular $b$. In this talk we will show how to solve the perturbed differential system with a certain stochastic averaging operator. As an application, we show that the stochastic transport equation driven by fractional Brownian motion has a unique solution when $u_0 \in L^{\infty}$ and $b$ is a possibly random $\alpha$-Hoelder continuous function for $\alpha$ large enough. This is a joint work with Massimiliano Gubinelli.

After a short break, at around 12:15h, we will continue with a second talk by

SPEAKER 2: Michel Nassif (ENS Rennes)

TITLE: Introduction to interacting particle systems

ABSTRACT: Interacting particle systems is a recently developed field in the theory of Markov processes with many applications: particle systems have been used to model phenomena ranging from traffic behaviour to spread of infection and tumour growth. We introduce this field through the study of the simple exclusion process. We will construct the generator of this process and we will give a convergence result of the spatial particle density to the solution of the heat equation. We will also discuss a variation of the simple exclusion process with proliferation.

Everyone is invited to participare. For more information and a longer abstract of the first talk in pdf format, please contact carina.geldhauser@dm.unipi.it