Research-Introduction to the Langlands program: local and global

Research

Number Theory Seminar

Introduction to the Langlands program: local and global

Abstract

The first part of this talk is about the local Langlands correspondence. This is a correspondence between complex representations of a reductive group over a local field and representations of the Weil-Deligne group to the L-group of G. I will describe the so-called “Desideratum”, which are the expected properties of this correspondence that uniquely determine it, e.g., preservation of discreteness, Plancherel measures, Gamma factors, and Local intertwining relation.

The second part of this talk is about Arthur’s multiplicity formula for classical groups. This gives a classification of irreducible discrete automorphic representations of classical groups over a number field in terms of irreducible cuspidal automorphic representations of general linear groups. I will introduce local A-packets, which are local ingredients for these global classifications.