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 observables in operational quantum mechanics.
Joint IAS/PU Number Theory
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 to prove a conjecture due to Hoffman giving a generating family for multiple zeta values, and a conjecture of Deligne and Ihara on the fundamental group of the projective line minus 3 points.
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.
I will report on progress towards the conjecture in the case of Shimura varieties attached to non-exceptional groups.