To be preceded by a reception in 348 Avery Hall from 3:15-3:50pm.
Equidistribution and Primes
We review briefly 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 geometric context of actions by morphisms on affine n-space and outline a theory that has been developed in this context and some applications to classical problems connected with Pythagorean triangles and Apollonian packings.The methods used to develop a combinatorial sieve in this setting involve automorphic forms, expander graphs and unexpectedly, arithmetic combinatorics.
About the Speaker
Peter Sarnak has made major contributions to to number theory, and to questions in analysis motivated by number theory. His interest in mathematics is wide-ranging, and his research focuses on the theory of zeta functions and automorphic forms with applications to number theory, combinatorics, and mathematical physics.
In the course of his career, he has served on the faculty of the Courant Institute of Mathematical Sciences of New York University, Stanford University and Princeton University. He is currently the Eugene Higgins Professor of Mathematics at Princeton, as well as Professor of Mathematics at the Institute for Advanced Study.
Professor Sarnak is the recipient of numerous honors. Among these are American Mathematical Society's Levi L. Conant and Frank Nelson Cole Prizes (2003 and 2005 respectively), the Polya Prize of the Society Industrial and Applied Mathematicians (1998) and a Sloan Fellowship (1983). In 2002, he was named a Member of the National Academy of Sciences and a Fellow of The Royal Society of London.
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