1. Background

Prerequisite: Linear algebra and calculus.

The purpose is to explore the audience on "algebraic combinatorics" without assuming any previous knowledge of combinatorics. I will try to propose many open problems hoping that some of them are accessible and solvable by the audience. (We encourage and emphasize the discussions on trying to solve these open problems among the audience.)

2. Outline

(The main topic)

Introduction to algebraic combinatorics. Topics will include: codes and designs on the sphere and on the association schemes. Connections with group theory and some representation theory will also be discussed. (I will try to discuss these topics without assuming any previous knowledge as much as possible.

Prof. Eiichi Bannai is a worldwide well-known mathematician working in algebraic combinatorics area. He had been professor in Ohio State University (US), Kyushu University (Japan) and  Shanghai Jiatong Univesity (China). He is passionate to supervise students and to teach young generation mathematicians. He had supervised 30 Ph.D students and numerous graduate and undergraduate students. 

3. Text Book

No text book will be used. We will use some parts of the book in Japanese: Introduction to Algebraic Combinatorics, by Eiichi Bannai, Etsuko Bannai and Tatsuro Ito, published by Kyoritsu Shuppan in 2016. (English version is now under translation and a preliminary draft of the English version will be made available to the audience.) Other reference books and papers will be explained after the course starts.