威斯尼斯人5158cc2021年数论及其应用暑期威斯尼斯人5158cc

时间及地点：2021年8月2-5日 每天上午8：00-12：00

                  （万大庆 8：00-10：00 ，向青 10：00-12：00 ）

                    腾讯会议：944 8691 9384     密码：202108

讲授人及课程名称：

万大庆（美国加州大学欧文分校）：Zeta functions over finite fields

向 青（南方科技大学）：Applications of character sums in combinatorics

摘要：This mini-course consists of two parts. In one part, we will define classical/moment/partial zeta functions over finite fields. Our basic questions include rationality of these zeta functions, cohomological trace formula, weight estimates, explicit degree and Betti number estimates, namely, the Weil type conjectures. Along the way, many examples and open problems will be presented. In the other part, we will first define Gauss sums, Jacobi sums, and more general character sums over finite fields. Then we give a few sample applications of character sums in combinatorics. These include: the connection between Gauss sums and Singer difference sets, p-ranks of Singer difference sets and difference sets from hyperovals, applications of incomplete Kloosterman sums in the recent constructions of Cameron-Liebler line classes in .

The lectures will be introductory and intuitively accessible to a general audience in number theory and applications of number theory in combinatorics.

承办单位：威斯尼斯人5158cc、交叉科学研究院

联系人：张俊 (junz@cnu.edu.cn)