Date & Time: Wednesday, 21 September, 2011
Venue: Ramanujan Hall
Title: Sub-Convexity and Quantum Unique Ergodicity
Speaker: Prof. Ravi Raghunathan , IIT Bombay
Abstract:The main part of the talk will be spent in explaining what the two terms in the title mean and how they are related.
The sub-convexity problem in the theory of L-functions is a weak form of the Generalised Lindelof Hypothesis, itself a weak form of the Grand Riemann Hypothesis.Quantum Unique Ergodicity first arose in a conjecture of Rudnick and Sarnak. A special case concerns the limiting behaviour of measures associated to certain special eigenfunctions of the Laplacian on the upper half-plane. This was recently settled by Soundarajan and Holowinsky.
If time permits I will try to say a little bit about the work of Elon Lindenstrauss (Fields Medal 2010) on the general conjecture.