Arithmetic Algebraic Geometry

这是数学领域的一个项目叫做数论。Katz教授将研究在有限域上定义的变量，特别是它们的上同调和L函数在这些变量上的零点分布。这是数学领域的一个项目叫做数论。这个项目的主要焦点可以描述为多项式方程的某些类型的解的研究，称为“模解”。计算机科学家对数论的许多应用都涉及这类解决方案。Katz教授正在考虑的问题涉及这样的解的数量，这个数量如何随着多项式的变化而变化，以及不同多项式的解集如何相关。

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.