BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Lecture 2 | The Hypergraph Container Method - Jozsef Balogh (Unive rsity of Illinois at Urbana-Champaign) DTSTART:20240801T133000Z DTEND:20240801T143000Z UID:TALK219253@talks.cam.ac.uk DESCRIPTION: \;In this survey we describe a recently-developed techniq ue for bounding the number (and controlling the typical structure) of fini te objects with forbidden substructures. This technique exploits a subtle clustering phenomenon exhibited by the independent sets of uniform hypergr aphs whose edges are sufficiently evenly distributed\; more precisely\, it provides a relatively small family of &lsquo\;containers&rsquo\; for the independent sets\, each of which contains few edges. We attempt to convey to the reader 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.In Lecture 1\, besides motivations\, we will focus on the graph container method\, in Lecture 2 s everal applications of the Hypergraph Container Lemma will be discussed\, and in Lecture 3\, the sketch of the proof of the \; Hypergraph Contai ner Lemma will be discussed. Certainly\, some adjustment based on Lecture 1 will be done on the later lectures. LOCATION:External END:VEVENT END:VCALENDAR