题目：Finite fields: selected topics related to game theory, combinatorics, Zeta functions, and general algebra

报告人：Fabrice ORGOGOZO, Centre national de la recherche scientifique（法国国家科学研究中心）

时间：2024年11月5日-11月7日（周二至周四每天）16: 00-17: 30

地点：第五教学楼5307教室

摘要：

In these three 90-minute lectures, requiring only a superficial knowledge of finite field theory, we will present, after a very elementary introduction, some connections with game theory (the quadratic closure of the field with 2 elements constructed by Conway), combinatorics (existence and explicit construction of de Bruijn sequences), and general algebra (triviality of the Brauer group of a finite field).

Other topics —finite projective planes, the connection between the game of Nim and Hamming codes, the Pólya-Vinogradov theorem, the average number of irreducible factors, Artin-Schreier(-Witt?) theory, etc.— will be covered, depending on the time and the speaker's mood.

The lectures will be in English, with slides in French, drawn from a forthcoming book on finite fields.