Speaker：Daqing Wan (University of California, Irvine)

Time：2025-10-20 16:30

Location：Conference Room S102 at Experiment Building at Haiyun Campus

Abstract:

Gauss periods are exponential sums over multiplicative subgroups of finite fields. They were introduced by Gauss (1801) to solve the ancient geometric problem of constructing regular n-gon using a compass and straightedge. Since then, Gauss periods have been studied extensively and have found applications in coding theory, graph theory and combinatorial design. In this expository lecture, we present a global overview of this subject. We view Gauss periods as a multi-set of complex numbers, p-adic numbers and algebraic numbers. We will discuss the many open problems and conjectures arising naturally in the process.