|Thursday 20 June 2019|
|Events for day: Wednesday 12 June 2019|
| 16:00 - 17:15 Mathematics Colloquium|
Reciprocity and Functoriality
I will discuss some number theoretic background to explain classical reciprocity laws of number theory. This will be an introduction to non-abelian reciprocity which generalizes Artin reciprocity map. I will do this in terms of complex representations of local Galois groups which are to parametrize irreducible admissible representations of GL(n,F), where F is a local field. This is called the Local Langlands correspondence (LLC) for GL(n) which has been established by Harris-Taylor, Henniart and Scholze in various forms. I will mention recent results in matching of different arithmetic (Artin) root numbers and L-functions with analytic ones ...