Title: Equidistribution and primes I
Speaker: Professor Peter Sarnak
Speaker Info: Princeton and IAS
Brief Description:
Special Note:
Abstract:
We review various classical problems concerning the existence of primes or numbers with few prime factors as well as some of the developments towards resolving these long standing questions. We then put these problems in a natural and general geometric context of actions on affine n-space and indicate what can be established there. The methods used to develop a combinatorial sieve in this context involve automorphic forms ,expander graphs and unexpectedly arithmetic combinatorics. Applications to the divisibilty of areas of Pythagorean triangles and of curvatures of circles in integral Apollonian packings will be given. In the first lecture will give a general overview (for a general audience),in the second lecture we discuss the interesting special cases for which the general theory of automorphic forms can be used effectively in the analysis and in the third lecture we explain the role of arithmetic combinatorics in dealing with the general problem.Date: Tuesday, January 22, 2008