BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Henry Towsner (Pennsylvania) DTSTART:20211020T130000Z DTEND:20211020T140000Z DTSTAMP:20260423T021103Z UID:WCS/35 DESCRIPTION:Title: Reg ularity Lemmas as Structured Decompositions\nby Henry Towsner (Pennsyl vania) as part of Warwick Combinatorics Seminar\n\n\nAbstract\nOne way of viewing Szemerédi's regularity lemma is that it gives a way of decomposin g a graph (approximately) into a structured part (the "unary" data) and a random part. Then hypergraph regularity\, the generalization to k-uniform hypergraphs\, can be viewed as a decomposition into multiple "tiers" of st ructure - a unary part as well as a binary part and so on\, and then final ly a random part.\n\nWe'll discuss how an analytic approach can make these decompositions exact instances of the conditional expectation in probabil ity\, and how these analytic proofs relate to combinatorial proofs with ex plicit bounds. Finally\, we'll discuss regularity lemmas for other mathema tical objects\, focusing on the example of ordered graphs and hypergraphs\ , and show how the "tiers of structures" perspective makes it possible to see regularity lemmas for other mathematical objects as examples of the re gularity lemma for hypergraphs.\n\n(No prior knowledge of the regularity l emma and its variants is assumed.)\n LOCATION:https://researchseminars.org/talk/WCS/35/ END:VEVENT END:VCALENDAR