报告人简介: Dhruv Mubayi 是美国University of Ilinois at Chicago数学系教授，是国际组合图论界知名专家。他是五本著名期刊的编辑，包括Journal of Combinatorial Theory (B)、Journal of Combinatorial Theory (A)、SIAM Journal on Discrete Mathematics组合图论界顶尖期刊。
Abstract: The subject of extremal set theory began with Sperner's theorem in 1928 and has since become a central field within combinatorics that has many applications to other areas of mathematics and computer science. In this series of lectures, we will begin by covering the classical results in the field and continue to the most recent developments in present day research. Our focus will be on general methods that apply to a variety of problems. These include compressions or shifting, Katona's circle method, shadows, random walks, algebraic techniques, delta systems, sampling and canonical Ramsey theory, and dependent random choice.
The only prerequisites are a strong undergraduate background in linear algebra, combinatorics and probability together with the mathematical maturity of a graduate student.