**Date & Time:** Tuesday, August 11, 2009, 14:30-15:30.

**Venue:** Ramanujan Hall

**Title:** Subconvexity of *L*-functions and Applications

**Speaker:** Ritabrata Munshi, Tata Institute of Fundamental Research

**Abstract:** Functional equation together with the Phragmén-Lindelöf Theorem gives bounds for *L*-functions inside the critical strip. This is called the trivial or the convexity bound. On the other hand the Riemann Hypothesis implies bounds which are much stronger. The "Subconvexity Problem" asks for bounds which are better than the trivial bound. Often such a nontrivial bound has interesting arithmetic applications. This talk will be a survey of such results.