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Thomas Haines (University of Maryland)
Endoscopic transfer of the Bernstein center

The Langlands-Shelstad theory of endoscopy plays a central role in the study of Shimura varieties and the Arthur-Selberg trace formula. The fundamental lemma and a deep consequence, endoscopic transfer, have now been established in works of Ngo, Waldspurger, and Hales. Both of these statements are identities involving orbital integrals of a function f on a p-adic group G and those of certain transfer" functions f^H on related groups H, called endoscopic. This talk will give background on the fundamental lemma, some of its variants, and the roles they played. Then I will describe a conjectural construction of a large class of matching functions in the Bernstein centers of G and H. This conjecture has been verified in some encouraging cases. The functions being transferred arise in connection with Shimura varieties with bad reduction, and some applications to that subject will also be briefly discussed.

Niranjan Ramachandran (University of Maryland)
Integral motives and zeta functions

The talk will be a survey of the joint work with Milne. The existing constructions of motives do not provide an integral category of mixed motives over a finite field. As a result, these constructions do not provide a motivic interpretation of the $p$-part of special values of zeta functions where $p$ is the characteristic. The talk will outline an approach to integral motives via the theory of the de Rham Witt complex.

Alice Silverberg (UC Irvine)
On elliptic curves with an isogeny of degree 7, and related questions

In joint work with Ralph Greenberg and Karl Rubin, we ask when the images of 7-adic representations of elliptic curves over Q with a rational subgroup of order 7 are as large as they can be. This leads to a construction of the family of all elliptic curves with a rational subgroup Galois-isomorphic to a given group of order 7, and also leads to a question about the rational points on a recalcitrant genus 12 curve.

Chandrashekhar Khare (UCLA)
Automorphic forms and Iwasawa theory

The method of Ribet and Wiles constructs unramified extensions of cylotomic extensions of totally real fields using automorphic forms. We will discuss how one one can construct ramified extensions, and the role these extensions play in questions about non-vanishing of p-adic regulators.