Geoffrey Grimmett: Self-avoiding walks on graphs and groups
The theory of self-avoiding walks (SAWs) originated in the study of polymerization, and has led to a number of prominent problems in various areas of mathematics including combinatorics, probability, and geometric group theory. This lecture is an overview of some of these problems, with emphasis on properties of the exponential growth rate of the counts of SAWs on transitive graphs, and especially on Cayley graphs of finitely generated groups. New results are joint with Zhongyang Li.
Professor Geoffrey Grimmett, University of Cambridge