UBC Mathematics Colloquium
(PIMS
lecture/colloquium)

##

## Quantum Unique Ergodicity and Number Theory

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

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 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.

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