Kannan SoundararajanAffiliation: Stanford University Email: ksound@stanford.edu
TALK 1
(
FOURTH RAMANUJAN COLLOQUIUM
)
:
Wednesday, March 24 in FAB 103 at 4:00pm Abstract: A fundamental problem in the area of quantum chaos is to understand the distribution of high eigenvalue eigenfunctions of the Laplacian on certain Riemannian manifolds. A particular case which is of interest to number theorists concerns hyperbolic manifolds arising as a quotient of the upper halfplane by a discrete "arithmetic" subgroup of SL_{2}(R) (for example, SL_{2}(Z), and in this case the corresponding eigenfunctions are called Maass cusp forms). In this case, Rudnick and Sarnak have conjectured that the high energy eigenfunctions become equidistributed. I will discuss some recent progress which has led to a resolution of this conjecture, and also on a holomorphic analog for classical modular forms. I will not assume any familiarity with these topics, and the talk should be accessible to graduate students. TALK 2: Mean values of multiplicative functions and applications Thursday, March 25 in LIT 339 at 10:40am Abstract: The pioneering results of Wirsing and Halasz describe the situations when the meanvalue of a multiplicative function can be large. Understanding the structure of such multiplicative functions has proved useful in applications to the PolyaVinogradov inequality, weak subconvexity bounds for Lfunctions, and to the quantum unique ergodicity problem. I will try and explain some of these results and applications. TALK 3: The distribution of values of zeta and Lfunctions Friday, March 26 in LIT 339 at 10:40am Abstract: I will survey what is known and expected about the distribution of values of Lfunctions. In particular, I will try to explain probabilistic models that describe the behavior of these functions. At the center of the critical strip, the probabilistic models arise from random matrix theory, and I will discuss the KeatingSnaith conjectures for moments of Lfunctions, and recent progress.
Last update made Wed Mar 17 12:02:49 EDT 2010.
