**Dipendra Prasad**

TIFR

November 10, 2016

**A relative Local Langlands correspondence, and geometry of parameter spaces.**:
For E/F quadratic extension of local fields, we consider the question of classifying irreducible admissible representations of G(E) which carry a G(F)-inv. linear form. Although in a certain generic sense, one expects a simple answer --- multiplicity 1, and exact characterization, the full answer is rather complicated --- and interesting, involving geometry of Langlands parameters. The colloquium talk will begin by reviewing the Local Langlands correspondence.