Thematic Programme:Arithmetic geometry and automorphic representations

This programme will focus on new research directions involving automorphic representations and their interplay with geometry and arithmetic, specifically, the arithmetic geometry of Shimura varieties and the cohomology of arithmetic groups. There has been important recent progress including:

• Arithmetic consequences of the progress on establishing the Gross-Prasad conjectures about certain branching laws for automorphic representations, in particular, applications to the arithmetic intersection theory of special algebraic cycles on products of orthogonal, and unitary Shimura varieties,
• new results on the geometry of integral models and local models of Shimura varieties, including those which are not moduli spaces for abelian varieties, and
• cohomology of the boundary of Shimura varieties: (residues of) Eisenstein series, mixed Hodge structures, and special values of automorphic L-functions.

The programme will bring together the leading experts involved in these developments, among which there are many important interconnections, to survey the present state of our knowledge and to foster new collaborative efforts.

The will be mini lecture courses as well as 1 - 2 talks every other day by participants in residence. In addition, embedded in the ongoing activities, there will be two workshops:

WS 1: Local models of Shimura varieties and related topics, April 19 - 25, 2015
WS 2 (incl. 2 mini lecture courses): Automorphic Forms - Geometry and Arithmetic, May 6 - 16, 2015