Bowen Lectures: Lecture 1 : Galois representations and automorphic forms - an introduction to the Langlands program

Lecture | February 22 | 4:10-5 p.m. | 50 Birge Hall

 Michael Harris, Columbia University

 Department of Mathematics

Automorphic forms are functions on a class of homogeneous spaces that arise naturally in geometry and number theory and that enjoy particularly strong symmetry properties (the simplest non-trivial example is the circle). Galois representations are efficient ways of packaging meaningful information about solutions to polynomial equations; the cohomology of algebraic varieties provides a rich supply of such packages. The Langlands program is predicated on the insight that these two branches of mathematics are to a large extent about the same thing.