Discrete Groups, Expanding Graphs and Pro-P Methods

Yale University, New Haven CT

Investigators

Abstract

The project looks at several seemingly unrelated problems from a unified perspective. It deals with questions of expansion of Cayley graphs of finite groups, eigenvalues of Riemannian manifolds and pro-p groups. Somewhat unexpectedly, methods and results from one field shed a new light on the other areas. The work is promising to be very interdisciplinary and should have, if successful, a serious impact on several mathematical fields, pure and applied. On the pure side, it is expected to have a completely new approach toward the Thurston conjecture on three- dimensional manifolds. On the applied side, it will bring a better understanding of expanding graphs, graphs which serve as basic building blocks for various communication networks.