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              MATHEMATICS DEPARTMENT
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            FIRST RAMANUJAN COLLOQUIUM
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                      by

            Professor Manjul Bhargava
              Princeton University

                      on

     Sums of two squares and the "290 theorem"

OPENING REMARKS: George E. Andrews
                 Evan Pugh Professor - Penn State Univ
                 Distinguished Visiting Professor - UF


DATE: Mon, Mar 19

TIME: 4:00 pm

ROOM: FAB 103

REFRESHMENTS: at 5:00 pm, in LIT 339

ABSTRACT: The famous "Four Squares Theorem" of Lagrange asserts that any
positive integer can be expressed as the sum of four square numbers. That
is, the quadratic form a^2 + b^2 + c^2 + d^2 "represents" all (positive)
integers. When does a general quadratic form represent all integers? When
does it represent all odd integers? When does it represent all primes? We
show how all these questions turn out to have very simple and surprising
answers. In particular, we describe the recent work (joint with Jonathan
Hanke, Duke University) in proving Conway's "290-Conjecture". This solves
a problem of Ramanujan on quadratic forms.

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              THREE MATHEMATICS SEMINAR TALKS

Following the Colloquium, Professor Bhargava will give three seminar
talks. The three seminars will work towards a precise statement and
proof of Ramanujan's quaternary problem and Conway's 290-Conjecture.

        JOINT NUMBER THEORY & COMBINATORICS SEMINARS

                         on

I. "The arithmetic of quadratic forms: an overview"
   Tue, Mar 20, at 12:50 pm in LIT 339


II. "Ramanujan's quaternary problem and finiteness theorems
    for quadratic forms"
    Tue, Mar 20, at 1:55 pm in LIT 339

III. "Effective finiteness theorems and the proof of Conway's
     290-conjecture"
     Wed, Mar 21, at 3:00 pm in LIT 339

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ABOUT THE SPEAKER: Professor Manjul Bhargava, at the young age of 32,
is one of the most eminent mathematicians in the world. When appointed
as Full Professor of Mathematics at Princeton University at the age
of 28, he was youngest to hold that high rank at Princeton. His phenomnal
mathematical career began early and recognitions have come in rapid
succession. He was the recipient of the Frank and Bennie Morgan Prize
of the American Mathematical Society (AMS) for undergraduate research in
1996. As an undergraduate at Harvard, he was Universtity Salutatorian and
winner of the Hoopes Prize. He then went to Princeton University to do
his PhD under the direction of Prof. Andrew Wiles of Fermat's Last
Theorem fame. Bhargava wrote a phenomenal PhD thesis in which he obtained
pathbreaking extensions of Gauss composition law for binary quadratic forms.
His thesis was published as four papers in the Annals of Mathematics.
For this and other work, he has received the AMS Blumenthal Prize in
January 2005, the Clay Mathematics Prize in November 2005, and the
First SASTRA Ramanujan Prize in December 2005.

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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.

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