| NUMBER THEORY SEMINAR: |
| KIRAN S. KEDLAYA (MIT): |
| Semistable reduction for overconvergent F-isocrystals |
| on Wednesday, May 21, 08, at 3 - 4 pm in Science Center, Room 507 |
| Abstract: As part of Berthelot's program for constructing a theory of coefficients in p-adic cohomology one repeatedly encounters the following problem: given an overconvergent F-isocrystal on variety X, show that one can pull back along an alteration to get an F-isocrystal which extends (with logarithmic singularities) to some proper variety. This amounts to eliminating some monodromy obstruction along all divisors on all blowups of X. We describe our recent solution of this problem, using a valuation-theoretic approach to reduce to a local calculation in relative dimension 1. |
| NUMBER THEORY SEMINAR: |
| TOSHIYUKI KOBAYASHI (Tokyo and Harvard): |
| Restriction of unitary representations of real reductive groups |
| on Wednesday, May 28, 08, at 3 - 4 pm in Science Center, Room 507 |
| Abstract: Branching problems ask how an irreducible representation of a group decomposes when restricted to its subgroup. Having an observation of bad features of branching problems in a general non-compact setting even for real reductive symmetric pairs, I will discuss how to find a nice setting for branching problems, and give an upper estimate on multiplicities. If time allows, some applications are also presented. |