Title: A computational motivation for topological Langlands correspondences.
Speaker: Andrew Salch
Speaker Info: Johns Hopkins University
Special Note: Different Room
We describe the most effective known method for computing the stable homotopy groups of spheres at odd primes; this uses formal modules over p-adic number rings, together with base-change properties of the "chromatic filtration," i.e., local cohomology on the moduli stacks of formal modules, to construct the Adams-Novikov E_2-term. A consequence of these methods is the appearance of denominators of special values of Artin L-functions in the orders of the stable homotopy groups of spheres. We describe the role this phenomenon plays in motivating the (still very speculative) study of topological Langlands correspondences.Date: Monday, March 09, 2009