The 2006 Alan Tayler Lecture was delivered by Prof Henri Berestycki of the Ecole des hautes Etudes en sciences sociales, Paris and University of Chicago.

Modelling Spatial Diffusion: from flames to social norms

Abstract

What do phase transitions in physics, propagation of flames, tumours, biological invasions, and the spread of criminality have in common? Diffusion is a ubiquitous mechanism in nature and in society, and, along with transport and reaction effects, is the main factor explaining changes or transitions in a wide array of systems. It lies at the core of systems where two or several possible states coexist, and accounts for certain states expanding or receding or giving rise to patterns. This lecture will describe some mathematical approaches to modelling spatial propagation and diffusion. These provide insights allowing one to understand better the underlying qualitative mechanisms. Properties of �reaction-diffusion equations� and their consequences will be especially examined, in the context of ecology of populations.