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X-WR-CALDESC:Events for Discrete Mathematics Group
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DTSTART:20220101T000000
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DTSTART;TZID=Asia/Seoul:20230314T163000
DTEND;TZID=Asia/Seoul:20230314T173000
DTSTAMP:20260419T114201
CREATED:20230120T011459Z
LAST-MODIFIED:20240707T073956Z
UID:6701-1678811400-1678815000@dimag.ibs.re.kr
SUMMARY:Stijn Cambie\, Recent progress on the Union-closed conjecture and related
DESCRIPTION:We give a summary on the work of the last months related to Frankl’s Union-Closed conjecture and its offsprings. The initial conjecture is stated as a theorem in extremal set theory; when a family F is union-closed (the union of sets of F is itself a set of $\mathcal F$)\, then $\mathcal F$ contains an (abundant) element that belongs to at least half of the sets. Meanwhile\, there are many related versions of the conjecture due to Frankl. For example\, graph theorists may prefer the equivalent statement that every bipartite graph has a vertex that belongs to no more than half of the maximal independent sets. While even proving the ε-Union-Closed Sets Conjecture was out of reach\, Poonen and Cui & Hu conjectured already stronger forms. \nAt the end of last year\, progress was made on many of these conjectures. Gilmer proved the ε-Union-Closed Sets Conjecture using an elegant entropy-based method which was sharpened by many others. Despite a sharp approximate form of the union-closed conjecture as stated by Chase and Lovett\, a further improvement was possible. In a different direction\, Kabela\, Polak and Teska constructed union-closed family sets with large sets and few abundant elements. \nThis talk will keep the audience up-to-date and give them insight in the main ideas. \nPeople who would like more details\, can join the Ecopro-reading session on the 14th of March (10 o’clock\, B332) as well. Here we go deeper in the core of the proofs and discuss possible directions for the full resolution.
URL:https://dimag.ibs.re.kr/event/2023-03-14/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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