Eric Vanden-Eijnden
Courant Institute
New York University

Abstract:

The dynamical behavior of many systems arising in physics, chemistry, biology, etc. is dominated by rare but important transition events between long lived states. Important examples include nucleation events during phase transition, conformational changes of macromolecules, or chemical reactions. Understanding the mechanism and computing the rate of these transitions is a topic that has attracted a lot of attention for many years. In this talk, I will discuss some recent theoretical developments for the description of rare events, as well as several computational techniques which allow to determine their pathways and rate. I will illustrate this concepts on the specific example of some reaction- diffusion equations driven by white-noise arising e.g. in the context of population dynamics, in micromagnetism, and in the description of the kinetics of phase transitions.