IPM Calendar 
Thursday 20 June 2019   Today  
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 ...