2008–2009 Erdős Colloquium:
Akshay Venkatesh

Geometry of numbers, old and new

Speaker: Professor Akshay Venkatesh, Stanford University
Date and time: Wednesday, March 11, 2009, 5:10–6:00 p.m.
Location: Little Hall, Room 101
Opening remarks: TBA

Abstract

The geometry of numbers is an old and beautiful method of solving equations in whole numbers using geometrical ideas. I shall discuss this method, illustrating with examples drawn from the theory of quadratic forms. I will then describe some modern descendants of the geometry of numbers; these draw on ideas from other mathematical fields including ergodic theory and harmonic analysis.

About the speaker

Professor Akshay Venkatesh has made far reaching contributions to a wide variety of areas of mathematics including number theory, automorphic forms, representation theory, locally symmetric spaces, and ergodic theory, by himself and in collaboration with several mathematicians. He received his PhD in 2002 from Princeton under the direction of Professor Peter Sarnak. In his thesis he realized the first step of a program proposed by Langlands of counting automorphic forms by analytic methods. He was C. L. E. Moore Instructor at MIT (2002–04) after which he was a Clay Research Fellow. He was appointed Associate Professor at Courant Institute, NYU in 2004. In 2007 he was recognized with the Salem Prize and the Packard Fellowship. And now at the very young age of 27, he has been elevated to the rank of Full Professor at Stanford University. In December 2008 he was awarded the SASTRA Ramanujan Prize.