Chvátal's Conjecture and Correlation Inequalities
报告专家：常帆 博士（南开大学）
报告时间：10月10日-10月14日每天上午9:30-11:00
报告地点：国家天元数学西南中心516
报告摘要：
This mini-course, given in 5 lectures, presents our recent proof of Chvátal's conjecture using Boolean function analysis. Posed in 1972, the conjecture states that every hereditary family of subsets of a finite set has a largest intersecting subfamily that is a star.We will first explain the equivalence between Chvátal's conjecture and a correlation conjecture of Friedgut, Kahn, Kalai and Keller for increasing Boolean functions, one of which is antipodal. We will then introduce the necessary background, including Fourier analysis on the discrete cube, influences, and covariance, and survey related developments in correlation inequalities. Finally, we will present the main ideas and details of our proof of a sharp correlation inequality relating covariance to Fourier coefficients and influences, and show how it implies the correlation conjecture and hence Chvátal's conjecture.The course is aimed at graduate students with a basic background in combinatorics and probability. All necessary tools from Boolean function analysis will be introduced. The new results are joint work with Hong Liu and Miao Liu.
专家简介：
Fan Chang is a Ph.D. student at Nankai University advised by Lei Yu. He received his M.Sc. in Mathematics from Shandong University in 2023 under Guanghui Wang's supervision. His research interests include analysis of Boolean functions, extremal and probabilistic combinatorics. His work has appeared in JCTA/B and SIDMA.
邀请人：王健
