Speaker: Professor Jozsef Balogh，University of Illinois

Title: On the container method

Language: Chinese

Time & Venue: 2025.06.19 10:00-11:00 南楼208

Abstract: In this survey type talk we describe a recently-developed technique for bounding the number (and controlling the typical structure) of finite objects with forbidden substructures. This technique exploits a subtle clustering phenomenon exhibited by the independent sets of uniform hypergraphs whose edges are sufficiently evenly distributed; more precisely, it provides a relatively small family of ‘containers’ for the independent sets, each of which contains few edges. We attempt to convey a general high-level overview of the method, focusing on a small number of illustrative applications in areas such as extremal graph theory, Ramsey theory, additive combinatorics, and discrete geometry, and avoiding technical details as much as possible.