短课：An Introduction to Additive Combinatorics
主讲人：赵永强（西湖大学）
时间：2024年5月10-12日，每天上午10:00-12:00，下午14:00-17:00
地点：苏州大学天赐庄校区维格堂119
短课内容：
Additive combinatorics is a branch of combinatorics that has been very active over the last thirty years. It studies, for example, adding together two subsets of a given abelian group and understanding the structure of the sum set. This new subject brings together ideas from harmonic analysis, ergodic theory, combinatorics, graph theory, probability theory and analytic number theory to prove extraordinary results, for example, Gowers' proof of the quantitative Szemeredi theorem and Green-Tao's theorem on arithmetic progressions in prime numbers.
In this short course, we will give a friendly introduction to this beautiful subject. The various topics we plan to discuss are as follows:
(1) Review of Fourier analysis over finite abelian groups;
(2) Polynomial Freiman-Ruzsa's theorem;
(3) The Balog-Szemeredi-Gowers theorem;
(4) Roth's theorem on 3-term arithmetic progressions (3-AP);
(5) The cat set problem, 3-AP over finite fields.
If time permits and the audiences have enough interests, we will also briefly discuss Gowers uniformity norms and the proof of the existence of 4-AP over finite fields.
This course is self-contained and should be accessible to advanced undergraduates or beginning graduate students.
主讲人简介：赵永强，西湖大学理学院特聘研究员。主要研究方向为数论与算术几何，具体包括：算术统计，数域类群torsion子群，代数簇上有理点和整点的分布，代数曲线的syzygy理论，图的谱理论及其与数论的关系等。
欢迎参加！
邀请人：张影