A Non-symmetric Kesten Criterion for Random Walks on Groups

Explore a mathematical lecture on non-symmetric random walks on countable groups and their relation to amenability. Delve into an extension of Kesten's famous 1959 result, which originally connected symmetric random walks to group amenability. Examine how this new research expands the concept to non-symmetric walks, potentially impacting various areas of mathematics including spectral theory and geometric group theory. Learn about the collaborative work between the speaker and Rhiannon Dougall, which aims to broaden our understanding of amenability dichotomies. Gain insights into the implications of this research for the study of Laplacian spectra on manifolds and critical exponents of discrete isometry groups.