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Ordway Lectures and Visitors

Ordway Lectures
  Oct 4—Oct 6, 2005
    David Vogan

 
  Mar 28—Apr 1, 2005
    Stuart Antman

  Sep 28—Oct 1, 2004
    Pierre-Louis Lions

 
  Apr 17–23, 2004
    Maxim Kontsevich

  Feb 24–26, 2004
    Hillel Furstenberg

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Other Math Seminars

Other UMN Seminars

David Vogan

Massachusetts Institute of Technology
Cambridge, MA

October 4 — October 6, 2005


The Local Langlands Conjecture

Local and global.
Tuesday, October 4, 2005 3:35pm, Vincent Hall 16

The goal of these lectures is to discuss the "local Langlands conjectures," and particularly what they tell you about representations of real Lie groups. To understand that, you need to know a little bit about the global Langlands conjectures: at least what "local" and "global" mean in this context. I'll illustrate with two examples: prime factorization of rational numbers, and classification of quadratic forms over ${\Bbb Q}$.

Representations of reductive groups.
Wednesday, October 5, 2005 3:35pm, Vincent Hall 16

A basic idea in linear algebra is to relate general matrices to diagonal ones. When the field isn't algebraically closed, this requires a generous interpretation of "diagonal" to take into account field extensions. A basic idea in representation theory is dual: to relate representations of matrix groups to characters of diagonal subgroups. Perhaps the most familiar example is the Cartan-Weyl theory parametrizing representations of a compact Lie group by characters of a maximal torus. I'll explain this example, and generalizations to matrix groups over local fields.

The local Langlands conjecture.
Thursday, October 6, 2005 3:35pm, Vincent Hall 16

In this lecture I'll explain how Langlands recast the description of representations from the second lecture---in terms of characters of diagonal subgroups---to make it a natural local piece of a description of some global arithmetic objects. Because the resulting conjecture relates representation theory to arithmetic, it allows these two subjects to inform each other. I'll conclude with some examples of how that has worked in the past, and of what it may suggest in the future.

www.math.umn.edu/ordway/2005/vogan/
Last Modified September 12, 2005
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