Arithmetical geometry and number theory - A conference in honor of N. Katz

American Institute Of Mathematics, Pasadena CA

Investigators

Abstract

Principal Investigator: Brian Conrey Proposal Number: DMS -0306938 Institution: American Institute of Mathematics Arithmetical geometry and number theory, a conference in honor of N. M. Katz Abstract: After the works of Weil, Grothendieck, and Deligne, the theory of zeta functions of varieties over finite fields has been a very powerful tool in number theory and geometry. Katz has been and continues to be a leading researcher in these areas and has championed their applications. His contributions range from exponential sums, monodromy groups and their representations, number theory, modular forms classical and p-adic, to arithmetic moduli problems. All of these areas are still very much at the center of current research. The PIs will conduct a 4 day conference on these connected areas. The timing will coincide with Katz' 60 th birthday. The conference will bring together many of the leading researchers in these fields to lecture on the latest developments. In addition to these advanced lectures the conference will also feature survey lectures and discussion sessions aimed for graduate students and postdocs. The combination of the mathematical fields of number theory and arithmetical geometry is concerned in part with the study of counting solutions to algebraic equations (such as Fermat's equation) where the solutions are to be whole numbers. The study of such problems requires some of the most sophisticated modern mathematical theories. The payoff for mastering and developing these theories is great. For instance, there are far-reaching applications to other areas of pure mathematics as well as to areas of applied discrete mathematics such as computer science, to the design of optimally efficient networks and to cryptography. This 4-day conference will feature this important mathematics, especially those aspects closest to the interests of N. M. Katz who is a world leader in these areas. Particular attention will be devoted to including graduate students and postdoctoral associates in all aspects of the conference. Survey lectures and formal discussion sessions which will be particularly useful to younger mathematicians will be a highlight of the conference.