We introduce recent work studying systems of diffusion that interact through their reflection term (local time). We discuss how the hydrodynamic limit of such systems, i.e. the large-scale behavior of the empirical process, will converge to a nonlinear PDE whose solution exhibits interaction with the past values at the boundary. If time allows, we will discuss aspects of the proofs and how the uniqueness of such PDEs follows from a stochastic representation.

**Date**: 17 June 2019, 12:00 (Monday, 8th week, Trinity 2019)**Venue**: Mathematical Institute

Woodstock Road OX2 6GGSee location on maps.ox**Speaker**: Clayton Barnes (Université de Neuchâtel)**Organising department**: Department of Statistics**Part of**: Probability seminar**Booking required?**: Not required**Audience**: Public- Editor: Christina Goldschmidt