Department Mathematik



Mathematisches Kolloquium

On Thursday November 29th, 2018, at 16:30h

Geoffrey Grimmett
(University of Cambridge, Downing College)

will give a talk in lecture hall A027 on

Self-Avoiding Walks on Graphs and Groups

Abstract: The problem of self-avoiding walks (SAWs) arose in statistical mechanics in the 1940s, and has connections to probability, combinatorics, and the geometry of groups. The basic question is to count SAWs. The so-called 'connective constant' is the exponential growth rate of the number of n-step SAWs. We summerise joint work with Zhongyang Li concerned how the connective constant depends on the choice of graph. This work includes equalities and inequalities for connective constants, and a partial answer to the so-called 'locality problem' for graphs and particularly Cayley graphs. A number of open problems remain.

Everyone is invited! Join us for coffee and tea in the common room (B448) half an hour before the talk.