University of Florida, Mathematics Department
THIRD
RAMANUJAN^{*}
COLLOQUIUM
by
Professor Dorian
Goldfeld^{**}
Columbia University
on
Multiple Dirichlet series
Date and Time: 4:00  5:00pm, Monday, February 23, 2009
Room: TUR L011
Refreshments: After the lecture in the Atrium (LIT 339)
OPENING REMARKS
by
TBA



Abstract:
This talk will be partly historical and aimed at a general
audience. Ramanujan was fascinated by the problem of counting primes.
He wrote several papers connected with the Riemann zeta function.
Dirichlet introduced generalizations of the Riemann zeta function
(now called Dirichlet Lfunctions) to prove that there exist
infinitely many primes in an arithmetic progression. In this talk we
introduce the theory of multiple Dirichlet series (MDS) which are
Dirichlet series in several complex variables. The main goal is to
construct MDS which have as many of the properties of the Riemann
zeta function as possible: meromorphic continuation; group of
functional equations; Euler product, etc. We shall outline the
development of the theory of MDS in recent years and focus on some
applications to moments of special values of Dirichlet series of one
complex variable. The talk will end with a description of a beautiful
class of MDS known as WMDS (Weyl group multiple Dirichlet series)
which can be constructed from any root system of a classical Lie group.
NOTE: After the Ramanujan colloquium, Professor Goldfeld will
give two Number
Theory Seminars on related topics at 12:50 pm
on Tues, Feb 24, and at 10:40am on Wed, Feb 25 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:
Dorian Goldfeld is one of the most eminent number
theorists in the world. He has made seminal contributions to analtyic
number theory, the theory of modular forms, automorphic functions,
and cryptography, among others. Together with Michael and Irish Anshel,
he founded the field of Braid Group Cryptography. In 1987 he was awarded
the Cole Prize of the American Mathematical Society for his solution
of Gauss' class number problem for imaginary quadratic fields. He
received his BA from Columbia University in 1967 and his PhD there
in 1969 under the supervision of Patrick Gallagher. He held positions
at Berkeley (Miller Instructorship, 196971), Insititute for Advanced
Study, Princeton (197374), MIT (197682), the University of Texas,
Austin (198285) and Harvard (198385) before returning to his alma mater
Columbia in 1985 as Professor.
He was a Sloan Fellow (1977  79) and received the Vaughn Prize in 1985.
He serves on the Editorial Board of Acta
Arithmetica and The Ramanujan Journal.
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
