To any essentially self-dual, regular algebraic (ie
cohomological) automorphic representation of GL(n) over a CM field
one knows how to associate a compatible system of l-adic
representations. These l-adic representations occur (perhaps
slightly...
We discuss a quantum counterpart, in the sense of the
Berezin-Toeplitz quantization, of certain constraints on Poisson
brackets coming from "hard" symplectic geometry. It turns out that
they can be interpreted in terms of the quantum noise of...
For GL(2) over Q_p, the p-adic Langlands correspondence is
available in its full glory, and has had astounding applications to
Fontaine-Mazur, for instance. In higher rank, not much is known.
Breuil and Schneider put forward a conjecture, which...
I will report on some recent work on multiple zeta values. I
will sketch the definition of motivic multiple zeta values, which
can be viewed as a prototype of a Galois theory for certain
transcendental numbers, and then explain how they were used...
The families of motives of the title arise from classical
one-variable hypergeometric functions. This talk will focus on the
calculation of their corresponding L-functions both in theory and
in practice. These L-functions provide a fairly wide...
A conjecture of Langlands-Rapoport predicts the structure of the
mod p points on a Shimura variety. The conjecture forms part of
Langlands' program to understand the zeta function of a Shimura
variety in terms of automorphic L-functions.
Let X a curve over F_q and G a semi-simple simply-connected
group. The initial observation is that the conjecture of Weil's
which says that the volume of the adelic quotient of G with respect
to the Tamagawa measure equals 1, is equivalent to the...
