Professor Mark Behrens from M.I.T. speaking about "Orientations and Eisenstein series"

Abstract: Using a theorem of Jacob Lurie, Tyler Lawson and I have associated cohomology theories of topological automorphic forms (TAF) to certain unitary Shimura varieties. These cohomology theories generalize the theory of topological modular forms (TMF). Mike Hopkins and his collaborators were able to show that TMF admitted a cannonical string (MO<8>) orientation. Their construction rested on the p-adic interpolation of the classical eisenstein series (due to Katz). In this talk I will describe the current state of affairs of a joint project with Hopkins to find orientations of the TAF theories. I will explain how orientations are related to p-adic L-functions. Our attempts are related to the existence and properties of the p-adic interpolation of scaler valued Eisenstein series on the associated shimura varieties.