Mahler tour AGR event: Thin integer matrix groups and the affine sieve

Host Institution:

University of Western Australia

Title of Seminar:

Thin integer matrix groups and the affine sieve

Speaker's Name:

Professor Peter Sarnak

Speaker's Institution:

Institute for Advanced Study, Princeton University

Time and Date:

Friday 12th August 2011, 1:30pm WST (3:30pm EST)

Seminar Abstract:

Infinite index subgroups of integer matrix groups like SL(n,Z) which are Zariski dense in SL(n) arise in geometric diophantine problems (eg. Integral Apollonian Packings) as well as monodromy groups associated with families of varieties. One of the key features needed when applying such groups to number theoretic problems is that the congruence graphs associated with these groups are "expanders". We will introduce and explain these ideas and review some recent developments especially those connected with the affine sieve.

This lecture is part of the Mahler lecture tour, further details here:

Seminar Convenor:


AGR IT support: