# abstract

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.