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) For n > 1, let $\pi, \pi'$ be two irreducible cuspidal automorphic representations of GL(n, A) where A denotes the adeles over Q. Let $L(s, \pi \times \pi')$ be the RankinSelberg Lfunction. If one of $\pi$ or $\pi'$ is self dual then it was shown by Moreno and Sarnak that the RankinSelberg Lfunction does not vanish at s = c+it when 1c is less than a positive fixed constant times a negative power of log(t +2). This is also called a standard zero free region. A standard zero free region for the Riemann zeta function was first obtained by de la Vallee Poussin (prime number theorem).
Currently, the best known zero free region for Rankin Selberg Lfunctions on GL(n) (in the non self dual case) is due to Brumley who has proved 1c is less than a fixed constant times a negative power of t +2. In joint work with Xiaoqing Li we obtain a standard zero free region in the non self dual case. 
November 13 
Kim Laine (Berkeley)
The security of genus 3 curves in public key cryptography has long been somewhat unclear. For nonhyperelliptic genus 3 curves Claus Diem found a way to exploit the geometry of the curve to speed up index calculus on the Jacobian, achieving an impressive running time of Õ(q). Unfortunately the algorithm suffers from massive memory requirements. 
November 20 
TBA TBA 
November 27 
THANKSGIVING BREAK

December 4 
TBA TBA 
December 11 
TBA TBA 