Dear colleagues, I would like to announce the following online seminar organized by the Probability group of the University of Pisa. The talks will be accessible under the link Join Microsoft Teams Meeting<https://teams.microsoft.com/l/meetup-join/19%3a17115d7f6ef44c5e91974362906cfc95%40thread.tacv2/1602238992289?context=%7b%22Tid%22%3a%22c7456b31-a220-47f5-be52-473828670aa1%22%2c%22Oid%22%3a%22dfd1e5f6-331d-43e0-a180-4bb6ce727fb7%22%7d> <https://aka.ms/JoinTeamsMeeting> Best regards, Giacomo <https://aka.ms/JoinTeamsMeeting> Tuesday, Oct. 13, 14:00 Speaker: Mauro Mariani Title: Quasi-invariant measures for a model of evolutionary biology Abstract: I will discuss a class of random models for the genetic evolution of a population of individuals with asexual reproduction. Formally, this is a diffusion process on an infinite-dimensional simplex. subject to absorption. It has been largely investigated in the past, both numerically and analytically as a model for the Muller's ratchet. We prove the existence and uniqueness of quasi-invariant measures describing the long-time behavior of the genetic distribution of the population, conditioned to non-extinction. The seminar is mostly based on https://arxiv.org/abs/2007.14715 Tuesday, Oct. 13, 15:00 Speaker: Marielle Simon Title: Hydrodynamic limit for a facilitated exclusion process Abstract: In this talk we will be interested in a one-dimensional exclusion process subject to strong kinetic constraints, which belongs to the class of cooperative kinetically constrained lattice gases. More precisely, its stochastic short range interaction exhibits a continuous phase transition to an absorbing state at a critical value of the particle density. We will see that the macroscopic behavior of this microscopic dynamics, under periodic boundary conditions and diffusive time scaling, is ruled by a non-linear PDE belonging to free boundary problems (or Stefan problems). One of the ingredients is to show that the system typically reaches an ergodic component in subdiffusive time. Based on joint works with O. Blondel, C. Erignoux and M. Sasada