# Press Release: NSF Invests a Million Dollars in Number Theory at the CUNY Graduate Center

The National Science Foundation (NSF) has awarded two grants totaling over a million dollars to Graduate Center mathematicians to further the study of number theory—the largest amount ever to be awarded in pure mathematics at CUNY. The NSF gave a Research Training Grant (RTG) in Number Theory (of approximately $870,000) to Distinguished Professor and Mina Rees Chair in Mathematics Victor Kolyvagin, Professor Kenneth Kramer, and Distinguished Professor Lucien Szpiro. Szpiro also received a Focus Research Grant (FRG) in Algebraic Dynamics for his Arithmetic Geometry Research Team (of approximately $192,000).

Number theory is the branch of mathematics investigating the properties of numbers in general and integers in particular. Started by Diophantus in ancient Alexandria in 200 B.C., it studies the structure of solutions to polynomial equations, often involving abstruse and dazzlingly complex proofs, as in the case of Fermat’s Last Theorem (formulated in 1637, but not proven until 1994). Number theory has recently had important applications for computer science and cryptography.

The RTG will provide complete support for three Graduate Center doctoral students for five years, as well as one post-doctoral associate, and partial support for other team members. The purpose of the RTG is to make the New York metropolitan area a premiere world center for the study of number theory—the grant is part of a three-university program with Columbia and NYU, both of which are receiving similar grants.

The RTG will also provide funding for programs, such as the joint Columbia-CUNY-NYU Number Theory Seminar, a weekly seminar held for the past several years, which rotates among the universities. This seminar was created by Dorian Goldfeld (Columbia), Peter Sarnak (Institute for Advanced Studies), and Lucien Szpiro and has been a successful collaboration between the three institutions, with large audience of 40 to 60 people. For more information on the seminar, visit http://math.gc.cuny.edu/seminars/jointnumbertheory.html

The FRG will support specific research led by Graduate Center faculty member Lucien Szpiro, who is doing important work in the field of Algebraic Dynamics. A new field recently classified by the American Math Society, Algebraic Dynamics is the study of problems in number theory from the point of view of dynamical systems, or systems that change.

The faculty members receiving the funding are well known for their contributions to number theory. Kolyvagin’s fundamental insights have had a huge impact on the field; in particular, his proof of the finiteness of the Tate-Shafarevich group played an important role in the path to the famous proof of Fermat's Last Theorem. Kramer’s insights into Abelian varieties (elliptic curves in many dimensions) are some of the deepest in recent years. Szpiro is known for his contribution to Falting’s proof of the Mordell conjecture and for Szpiro’s conjecture, concerning the relationship between the conductor and the discriminant in an elliptic curve.

The Graduate Center is devoted primarily to doctoral studies and awards most of the City University of New York’s Ph.D.s. An internationally recognized center for advanced studies and a national model for public doctoral education, the school offers more than thirty doctoral programs as well as a number of master’s programs. Many of its faculty members are among the world’s leading scholars in their respective fields, and its alumni hold major positions in industry and government, as well as in academia. The Graduate Center is also home to more than thirty interdisciplinary research centers and institutes focused on areas of compelling social, civic, cultural, and scientific concerns. Located in a landmark Fifth Avenue building, the Graduate Center has become a vital part of New York City’s intellectual and cultural life with its extensive array of public lectures, exhibitions, concerts, and theatrical events. Further information on the Graduate Center and its programs can be found at www.gc.cuny.edu.

Submitted on: DEC 1, 2009

Category: Mathematics | Press Room