Explore the profound impact of the KKL Theorem in mathematics through this 45-minute lecture by Ehud Friedgut, presented by the International Mathematical Union. Delve into the world of hypercontractivity, graph properties, and isoperimetric inequalities. Examine the Junta theorem and its applications to dictatorship and t-intersecting families. Investigate the Sès-Simonovits conjecture and its resolution. Discover the connections between graph products, traffic lights, and hypergraph theory. Gain insights into the fascinating realm of intersecting families of permutations and their mathematical implications.
Overview
Syllabus
Intro
Influences
KKL Theorem
Introducing: hypercontractivity (Bonami-Beckner inequality)
An application: thresholds for graph properties
Isoperimetric inequalities and juntas
Junta theorem (F,97)
Dictatorships
t-intersecting families (F' 2008)
Sès-Simonovits conjecture: A-intersecting
Ellis-Filmus-F 2012
Graph products and traffic Lights
Alon-Dinur-F-Sudakov
Number of copies of one hypergraph in another
Intersecting families of permutations
Taught by
International Mathematical Union
