Arithmetic Algebraic Geometry

Princeton University, Princeton NJ

Investigators

Abstract

This is a project in the area of mathematics called number theory. Professor Katz will investigate varieties defined over finite fields, in particular their cohomology and the distribution of the zeros of L functions on such varieties. This is a project in the area of mathematics called number theory. The main focus of this project can be described as the study of certain kinds of solutions to polynomial equations called "modular solutions." Many of the applications computer scientists have for number theory involve these kinds of solutions. Professor Katz is considering questions involving the number of such solutions, how this number changes as the polynomials change, and how the solution sets of different polynomials are related.