University of Florida, Mathematics Department
FOURTH
RAMANUJAN^{*}
COLLOQUIUM
by
Professor
Kannan Soundararajan
^{**}
Stanford University
on
Quantum Unique Ergodicity and Number Theory
Date and Time: 4:00  5:00pm, Wednesday, March 24, 2010
Room: FAB 103
Refreshments: At 3:30pm in the Atrium (LIT 339)



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.
NOTE: After the Ramanujan colloquium, Professor Soundararajan
will
give two
Number Theory Seminars
on related topics at 10:40am, Thursday March 25 and Friday March 26
in LIT 339 (The Atrium).

^{*}
ABOUT RAMANUJAN: Srinivasa Ramanujan (18871920), a selftaught genius
from South India, dazzled mathematicians at Cambridge University by
communicating bewildering formulae in a series of letters. G. H. Hardy
invited Ramanujan to work with him at Cambridge, convinced that
Ramanujan was a "Newton of the East"! Ramanujan's work has had a
profound and wide impact within and outside mathematics. He is considered
one of the greatest mathematicians in history.
^{**}
ABOUT THE SPEAKER:
Professor Kannan Soundararajan is perhaps the top analytic number theorist
in the world under the age of 40. He has made outstanding contributions to
multiplicative number theory, the theory of the Riemann zeta function, Dirichlet
Lfunctions, and the theory of automorphic forms. Even as an undergraduate at
the University of Michigan, he did very fundamental research and was recognized
with the Morgan Prize of the American Mathematical Society for Undergraduate
Research the very first year that prize was instituted. After completing his PhD
at Princeton, he was awarded the prestigious American Institute of Mathematics
Fellowship, the very first year that was instituted. Then in 2005, he was the
recipient of the First SASTRA Ramanujan Prize given to mathematicians not
exceeding the age of 32 for pathbreaking contributions to areas influenced by
Srinivasa Ramanujan. In addition, he is a winner of the Salem Prize in analysis.
He is currently Professor at Stanford University. Very recently, in collaboration
with Roman Holowinsky, he solved an important case of the Quantum Unique
Ergodicity Conjecture of Rudnick and Sarnak and his talks will report on this
work among other things.
ABOUT THE SPONSOR: Evan Pugh Professor George Andrews of The Pennsylvania
State University is the world's premier authority in the theory of partitions
and work of the Indian mathematical genius Srinivasa Ramanujan combined.
He is a Member of the National Academy of Sciences.
He has close ties
with the UF Mathematics Department which has one of the strongest programs
on mathematics related to Ramanujan's work. He was a recipient of an
Honorary Doctorate from UF in December 2002. Since 2005, he is a Distinguished
Visiting Professor each year in the Spring term in the Mathematics Department.
He is currently President of the American Mathematical Society.
Ramanujan Colloquium *
University of Florida *
Mathematics *
Contact Info
