James Arthur, University of Toronto
Thomas Haines, University of Toronto
Robert Kottwitz, University of Chicago
George Pappas, Michigan State University

Overview:

This workshop will concern problems in number theory, algebraic geometry, and representation theory that arise in the study of reductions of Shimura varieties modulo primes, and related spaces. The topics to be discussed have a particular importance for the Langlands correspondence (in its local, global, and geometric avatars), which will serve as a unifying theme. The goal is to foster communication between experts working in various fields, and to present to a wider audience the central ideas that have contributed to recent progress. More specifically, there will be lectures related to the following topics:

The construction of well-behaved integral p-adic models for Shimura varieties.

The calculation of the sheaves of vanishing cycles and of the local factor of the Hasse-Weil zeta function.

The theory of p-adic uniformization.

Relations with affine Grassmanians, moduli of vector bundles and the geometric Langlands conjectures.

Related problems in representation theory and harmonic analysis: p-adic Hecke algebras, the Arthur-Selberg trace formula and the fundamental lemma.

Reductions of Shimura varieties in relation with the local and global Langlands conjectures; applications to the construction of Galois representations.

For further information please contact shimura@fields.utoronto.ca