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DTSTART;TZID=Asia/Seoul:20250604T163000
DTEND;TZID=Asia/Seoul:20250604T173000
DTSTAMP:20260416T222814
CREATED:20250319T134432Z
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UID:10696-1749054600-1749058200@dimag.ibs.re.kr
SUMMARY:Denys Bulavka\, Strict Erdős-Ko-Rado Theorems for Simplicial Complexes
DESCRIPTION:The now classical theorem of Erdős\, Ko and Rado establishes\nthe size of a maximal uniform family of pairwise-intersecting sets as well as a characterization of the families attaining such upper bound. One natural extension of this theorem is that of restricting the possiblechoices for the sets. That is\, given a simplicial complex\, what is the size of a maximal uniform family of pairwise-intersecting faces. Holroyd and Talbot\, and Borg conjectured that the same phenomena as in the classical case (i.e.\, the simplex) occurs: there is a maximal size pairwise-intersecting family with all its faces having some common vertex. Under stronger hypothesis\, they also conjectured that if a family attains such bound then its members must have a common vertex. In this talk I will present some progress towards the characterization of the maximal families. Concretely I will show that the conjecture is true for near-cones of sufficiently high depth. In particular\, this implies that the characterization of maximal families holds for\, for example\, the independence complex of a chordal graph with an isolated vertex as well as the independence complex of a (large enough) disjoint union of graphs with at least one isolated vertex. Under stronger hypothesis\, i.e.\, more isolated vertices\, we also recover a stability theorem. \nThis talk is based on a joint work with Russ Woodroofe.
URL:https://dimag.ibs.re.kr/event/2025-06-04/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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