Date: | January 31 (Mon), 2005, 15:00-17:00 |
Speaker: | Yves ANDRE (Ecole Normale Superieure, France) |
Title: |
On p-adic differential equations, q-difference equations, Galois
representations and Hasse-Arf filtrations
We shall first sketch two relatively well-known analogies: between differential equations and q-difference equations on one hand, and between Galois representations of local fields of characteristic p and complex linear differential equations over a punctured disk on the other hand. In the p-adic world, it turns out that both analogies can be substantially strengthened, and we shall explain how they eventually lead to some equivalences of categories. The three categories under consideration carry natural filtrations of ``Hasse-Arf type", which turn out to correspond to each other despite their very different natures. A byproduct of the theory is that every p-adic differential module defined over an infinitesimally thin annulus of outer radius one, and which is invariant (up to isomorphism) under raising the variable x to the p-th power, can be canonically deformed into a family of q-difference modules over the annulus, parametrized by a p-adic number q close to 1. In this family, the fibre at q is isomorphic to the image of the fiber at q^p under raising the variable x to the p-th power. |
Room: | RIMS, Room 206 |
Date: | October 10 (Fri), 2003, 15:00-17:00 |
Speaker: | Minhyong Kim (University of Arizona) |
Title: | On twisted p-adic mapping telescopes |
Room: | RIMS, Room 206 |
Date: | January 27 (Mon), 2003, 13:30-15:30 |
Speaker: | Ludmil KATZARKOV (University of California at Irvine) |
Title: |
Algebro geometric methods in topology
In this talk, we will introduce some classical algebro geometric invariants (braid factorization) in topology. We will demonstrate how the braid factorization helps in computing symplectic invariants on some examples. |
Room: | RIMS, Room 206 |
Date: | January 24 (Fri), 2003, 16:00-18:00 |
Speaker: | Ben MOONEN (University of Amsterdam) |
Title: |
Serre-Tate theory for PEL moduli spaces
The goal of this talk is to discuss a generalization of Serre-Tate theory of ordinary moduli to certain Shimura varieties. We shall discuss several possible definitions of ``ordinary objects'', and we show that these notions nicely agree. After that we discuss the deformation theory of ordinary objects. The structure of the deformation space heavily depends on the number of slopes (which, other that in the classical theory, can be arbitrary). If the number of slopes is 3 or more, we are led to introduce a new "group-like" structure, called a cascade. We shall illustrate the general theory with some concrete examples. |
Room: | RIMS, Room 206 |
Date: | December 9 (Mon), 2002, 15:00-17:00 |
Speaker: | Alexander LUBOTZKY (Hebrew University) |
Title: |
Counting congruence subgroups
``Subgroup growth'' deals with counting finite index subgroups of a group. This theory led to counting congruence subgroups in arithmetic groups. The latter counting is a kind of ``non-commutative analytic number theory'' where ``counting primes'' on one hand and delicate finite group theory, on the other hand, are combined. We will present the main counting results, applications to group theory and connections with the congruence subgroup problem and the structure of the fundamental groups of hyperbolic manifolds. |
Room: | RIMS, Room 206 |
Date: | July 30 (Tue), 2002, 15:00-17:00 |
Speaker: | Noam ELKIES (Harvard University, USA) |
Title: | Points of low canonical height on elliptic curves and surfaces |
Room: | RIMS, Room 202 |