September 11 
Peter Schneider (University of Munster and MSRI) The talk will describe joint work with L. Berger and B. Xie
in which we build, for a finite extension L of Q_p, a new theory of
(phi,Gamma)modules whose coefficient ring is the ring of holomorphic
functions on the rigid character variety of the additive group o_L, resp. a
"Robba" version of it. 
October 2 
NO SEMINAR

October 9 
NO SEMINAR

October 16 
NO SEMINAR

October 23 
Michelle Manes (University of Hawai'i) Given a global field K and a rational function f(x) defined over K, one may take preimages of 0 under successive iterates of f, and thus obtain an infinite tree by assigning edges according to the action of f. The absolute Galois group of K acts on the tree, giving a subgroup of the group of all tree automorphisms. 
October 30 
Valentijn Karemaker (University of Utrecht) Let G denote an algebraic group over Q and K and L two number fields.
Assume that there is a group isomorphism of points on G over the adeles of
K and L, respectively. We establish conditions on the group G, related to
the structure and the splitting field of its Borel groups, under which K
and L have isomorphic adele rings. Under these conditions, if K or L is a
Galois extension of Q and G(A_K) and G(A_L) are isomorphic, then K and L
are isomorphic as fields. As a corollary, we show that an isomorphism of
Hecke algebras for GL(n) (for fixed n > 1), which is an isometry in the L^1 norm over two number fields K and L that are Galois over Q, implies that the fields K and L are isomorphic. This can be viewed as an analogue in the theory of automorphic representations of the theorem of Neukirch that the absolute Galois group of a number field determines the field if it is Galois over Q.

November 6 
Dorian Goldfeld (Columbia University) TBA 
November 13 
Kim Laine (Berkeley) TBA 
November 20 
TBA TBA 
November 27 
THANKSGIVING BREAK

December 4 
TBA TBA 
December 11 
TBA TBA 