## UNIVERSITY OF PENNSYLVANIA

## Department of Mathematics

Fall 2006 -Hans Rademacher Lectures in Mathematics

Peter Sarnak

Department of Mathematics

Princeton University

will speak on

## Equidistribution and Primes

Problems of existence of the (infinitely many) primes satisfying constraints, for example, twin primes or primes in progressions, have fascinated mathematicians for centuries. While many such problems remain unsolved, there have been fine achievements. After reviewing some of these we discuss some of the powerful methods that have been developed. These include analytic tools, specifically L-functions and also sieve methods. The latter are particularly effective for producing almost primes. The traditional viewpoint for these problems in general is to search for primes lying on varieties. However, this is necessarily limited by the lack of understanding of integral points. The point of view that we will develop is that these problems are naturally associated with finding primes on orbits of a group acting on Z^n and for which a theory can be developed.

Review of some old and recent achievements and basic conjectures

Tuesday....September 19, 2006....3:30pm....A8 DRL

Sieve methods and some applications

Wednesday....September 20, 2006.....4:30pm...A6 DRL

Equidistribution in integer orbits

Expander and congruence graphs

Thursday....September 21, 2006....4:30pm...A2 DRL

(lecture will end at 6:00pm)

Previous Rademacher Lecturers

Lectures will be held in the David Rittenhouse Laboratory,

S.E. corner of 33rd and Walnut Streets, Philadelphia, PA.

Tea: 4E17 DRL at 3:00PM on Tuesday.

Tea on Wednesday and Thursday will be at 4:00PM.For further information, please call the Department of Mathematics at the University of Pennsylvania - 215-898-8627.