Sum-Product Estimates, Expanders, and Sieving

COMPUTER SCIENCE/DISCRETE MATH II
Topic:Sum-Product Estimates, Expanders, and Sieving
Speaker:Alex Gamburd
Affiliation:University of California at Santa Cruz
Date:Tuesday, December 19
Time/Room:10:30am - 12:30pm/S-101

We prove that Cayley graphs of SL_2(Z/qZ) are expanders with respect to the projection of any fixed elements in SL_2(Z) generating a non-elementary subgroup. This expansion property plays crucial role in establishing almost prime version of "SL_2(Z) Dirichlet Theorem". Joint work with Jean Bourgain and Peter Sarnak.