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
Tea will be served at 4:30pm