Phillip Griffiths Institute for Advanced Study, School of Mathematics Title: Special values of arithmetic automorphic cohomology classesAbstract: 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. |