Special PIMS/WMAX Postdoctorial Colloquium: David Roe

Abstract:

The Langlands correspondence relates global Galois  
representations with automorphic representations; the local  correspondence works at each prime.  For any reductive group $G$ over  a local field $K$ we construct a complex reductive group $^LG$.  For  any homomorphism from the Galois group of $K$ to $^LG$ (called a  Langlands parameter) we then construct a set of representations of  
$G(K)$ (called an L-packet).  I will make these constructions explicit  in the case that the Langlands parameter is discrete, tamely ramified  and regular and that $G$ is the unitary group associated to a tame  extension of $K$.