Columbia Mathematics Department Colloquium


Expliciting the local Langlands correspondence


 Guy Henniart  

                                                               University of Paris-Sud



All elliptic curves over Q are now known to be modular, and this implies Fermat's Last theorem.

Those results belong to the framework of the Langlands program, which conjectures precise links

 between Galois representations and modular forms (for GL(2)), or more generally automorphic

forms for reductive groups G. There is a local counterpart, presumably easier, and actually proved,

over the field Q_p of p-adic numbers, relating Galois representations of  degree n with linear

(infinite dimensional usually) representations of GL(n, Q_p).  Both sides, when n is prime to p for

 example, have a very reasonable explicit description. But describing the Langlands correspondence

explicitly is a nightmare. Please come and share!


  Nov. 17th, Wednesday, 5:00-6:00 pm

Mathematics 520

Tea will be served at 4:30pm