I work on questions raised by the Langlands program, which lies in the intersection of number theory, representation theory, algebraic and differential geometry, and analysis. More precisely, the following topics are of interest to me:
- The representation theory and harmonic analysis on locally compact groups, particularly the groups of rational points of real and p-adic reductive groups. One would like to know how to construct such representations, how to compute their character function, and how to find simple spaces of parameters for them.
- The cohomology of Galois groups and related objects. My main interest here is to understand and refine the concept of an inner form of a connected reductive group over a local or global field.
- The description of the automorphic spectrum of reductive groups over global fields. Here one would like to understand automorphic representations of a given group, relate them to those of other groups, and ultimately describe them intrinsically in terms of the description of their local components.