Langlands correspondence for GL_2"

Abstract:

Fix p a prime number. The local Langlands correspondence for GL_n is a bijection

between some n-dimensional Galois representations and some representations of GL_n(F)

over the complex numbers where F is a local field such as the field of p-adic numbers Qp.

Since recently, people have started studying representations of such groups over fields

of characteristic p. It turns out that essentially all the methods and results of the complex

case collapse and new phenomena emerge. I will try to explain (part of) what is known for GL_2.

Fix p a prime number. The local Langlands correspondence for GL_n is a bijection

between some n-dimensional Galois representations and some representations of GL_n(F)

over the complex numbers where F is a local field such as the field of p-adic numbers Qp.

Since recently, people have started studying representations of such groups over fields

of characteristic p. It turns out that essentially all the methods and results of the complex

case collapse and new phenomena emerge. I will try to explain (part of) what is known for GL_2.

September 26th, Wednesday, 5:00-6:00 pm

Mathematics
520

Tea
will be served at 4:30pm