Department of Mathematics  
Seminars  
Address: Mathematics
25337

Caltech  Pasadena, CA 91125
Telephone: (626) 3954335  Fax: (626) 5851728 
Project MATHEMATICS!  Caltech Home 
Mathematics
Colloquium
2013  2014 
Tuesday,
November 26, 2013 4:00 p.m. // 151 Sloan Alex Kontorovich (Yale)  LocalGlobal Problems in Orbits Abstract: We will discuss some natural problems in arithmetic and reformulate them as localglobal principles for orbits of integer matrix groups. Applications include Zaremba's Conjecture, McMullen's "Arithmetic Chaos" Conjecture, and the LocalGlobal Conjecture for Apollonian Gaskets. The main tools are expander graphs, bilinear forms, and bounds for exponential sums. 
