Phillip Griffiths
Institute for Advanced Study, School of Mathematics

Title: Special values of arithmetic automorphic cohomology classes

Abstract: Mumford-Tate groups are the basic symmetry groups of Hodge theory,
encoding both the Q-structure and the Hodge structure. Mumford-Tate domains are
the parameter spaces for families of polarized Hodge structures whose generic member
has a given reductive Q-algebraic group as Mumford-Tate group. In joint work with
Mark Green and Matt Kerr, those reductive Q-algebraic groups that arise as Mumford-
Tate groups, and more importantly the ways in which they may be so realized, have
been classified. The corresponding Mumford-Tate domains have rich geometric and
arithmetic structures, and in some very special cases there have emerged connections to
non-classical aspects of automorphic representation theory. This talk will give a general
overview of the above developments.