BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nitya Mani (UBC-O hosted) (MIT) DTSTART:20241107T220000Z DTEND:20241107T230000Z DTSTAMP:20260513T193650Z UID:SFUOR/42 DESCRIPTION:Title: T etrahedron intersecting families of hypergraphs\nby Nitya Mani (UBC-O hosted) (MIT) as part of PIMS-CORDS SFU Operations Research Seminar\n\nLec ture held in ASB 10908.\n\nAbstract\nAn $H$-intersecting family of 3-unifo rm hypergraphs on $n$ labelled vertices is a family of hypergraphs $\\math cal{F}$ such that for any pair of hypergraphs $G_1\, G_2 \\in \\mathcal{F} $\, the intersection $G_1 \\cap G_2$ contains a copy of $H$ as a subgraph. One can construct a large such family $\\mathcal{F}$ by choosing all of t he hypergraphs that contain a fixed copy of $H$\, a family with size $2^{{ n \\choose 3} - e(H)}$. Understanding for which cases such a family is asy mptotically maximal is a very old and well-studied question\, and it has b een conjectured that this lower bound is tight whenever $H$ is a complete graph. The case of triangle intersecting families of graphs was studied by Shearer and was one of the first application's of Shearer’s entropy ine quality to a combinatorial problem. This triangle-intersecting problem was fully resolved by Ellis\, Filmus\, and Friedgut\, and more recently the c ase of $K_4$-intersecting graphs was resolved by Berger and Zhao\, both us ing linear programming bounds. Despite this progress\, understanding the m aximal size of an $H$-intersecting family remains open for every other com plete (hyper)graph. In join work with Owen Zhang\, we resolve the case of $K_5$-intersecting families and provide the first resolution of an instanc e in the hypergraph setting\, showing that the conjecture holds for tetrah edron-intersecting families of 3-uniform hypergraphs.\n LOCATION:https://researchseminars.org/talk/SFUOR/42/ END:VEVENT END:VCALENDAR