**Date & Time:** Wednesday, September 24, 2014, 16:00-17:00.

**Venue:** Ramanujan Hall

**Speaker:** Muthu Krishnamurthy, University of Iowa

**Title:** Converse Theorems

**Abstract:** I will discuss my recent work with Andy Booker on Converse Theorems. A typical converse theorem gives a characterization of modular forms, or more generally (higher rank) automorphic forms, in terms of analytic properties of various twisted L-functions associated to them. Besides their applications in the Langlands program, they validate Langlands' philosophy that automorphic forms are the right source for L-functions with nice analytic properties. Over the years, many people have worked on reducing the size of the twisting set in converse theorems. We take a slightly different approach wherein we try to reduce the analytic properties required of the twists rather than the twisting set itself.