摘要: The problem of determining the independence number of (hyper)graphs has tight connections to questions in discrete geometry, coding theory, number theory, theoretical computer science and combinatorics. One of the most famous early examples is the result of Komlos-Pintz-Szemeredi from 1982 on the independence number of 3-uniform hypergraphs which made important progress on the decades old Heilbronn problem. I will begin by explaining this result and some of these connections. I Will then describe recent work in this area which shows that hypergraphs have a significantly different behaviow than graphs when it comes to independent sets. This answers a question posed by Ajtai-Erdow-Komlos-Szemeredi (1981), and disproves conjectures of deCaen (1986),Frieze and the speaker (2007), and several others.

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。