The Tamagawa Number Formula for Affine Kac-Moody Groups (joint work with D. Kazhdan)
Event details
| Date | 07.03.2016 |
| Hour | 16:15 › 17:30 |
| Speaker | Prof. Alexander Braverman, University of Toronto |
| Location | |
| Category | Conferences - Seminars |
Let G be an algebraic semi-simple group (e.g. G = SL(n)). Let also F be a global field (e.g. F = Q) and let A denote its adele ring. The "usual" Tamagawa number formula (proved by Langlands in 1966) computes the (suitably normalized) volume of the quotient G(A)/G(F) in terms of values of the zeta-function of F at certain numbers, called the exponents of G (these numbers are equal to 2, 3,…, n when G = SL(n)). When F is the field of rational functions on an algebraic curve X over a finite field, this computation is closely related to the so called Atiyah-Bott computation of the cohomology of the moduli space of G-bundles on a smooth projective curve.
After explaining the above results I am going to present a (somewhat indirect) generalization of the Tamagawa formula to the case when G is an affine Kac-Moody group and F is a function field. Surprisingly, the proof heavily uses the so called Macdonald constant term identity. We are going to discuss possible (conjectural) geometric interpretations of this formula (related to moduli spaces of bundles on surfaces).
After explaining the above results I am going to present a (somewhat indirect) generalization of the Tamagawa formula to the case when G is an affine Kac-Moody group and F is a function field. Surprisingly, the proof heavily uses the so called Macdonald constant term identity. We are going to discuss possible (conjectural) geometric interpretations of this formula (related to moduli spaces of bundles on surfaces).
Practical information
- General public
- Free
Organizer
- Prof. Hongler