|COMPUTER SCIENCE/DISCRETE MATH II|
|Topic:||Sum-Product Estimates, Expanders, and Sieving|
|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.