Colloquium: James Arthur
The third talk in our colloquium series is coming up:
| Speaker |
James Arthur, University of Toronto |
| Time |
3:30pm Thursday, March 9, 2006 |
| Title |
Weighted Orbital Integrals and the Langlands Program |
| Place |
Hoyt Auditorium |
Abstract
The Langlands program, at the most basic level, involves the study of finite
dimensional linear representations of the Galois group of the algebraic closure
of the rational numbers. These represenations have become increasingly
important; for example, Wiles' celebrated proof of Fermats' Last Theorem rests
on a result for linear represenations of dimension 2. Linear representations
naturally give rise to trace formulas (the trace here being a generalization of
the usual trace of a linear transformation). Weighted orbital integrals are the
terms on the geometric side of the trace formula. A deeper understanding of
their properties is becoming an increasingly important ingredient for progress
in the Langlands program. We shall begin with a brief and informal description
of the general goals of the Langlands program. We shall then describe in
elementary terms how weighted orbital integrals arise. Finally, we shall
outline the solution of a comparison problem for weighted orbital integrals on
different real Lie groups.
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