UBC Mathematics Colloquium

Kannan Soundararajan

(PIMS lecture/colloquium)

Quantum Unique Ergodicity and Number Theory

Fri., April 16, 2010, 3:00pm, MATX 1100


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 half-plane 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 equi-distributed.  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.

Back to the colloquium page.