BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Xizhi Liu (University of Illinois at Chicago) DTSTART:20210517T140000Z DTEND:20210517T150000Z DTSTAMP:20260423T052329Z UID:EPC/70 DESCRIPTION:Title: A u nified approach to hypergraph stability\nby Xizhi Liu (University of I llinois at Chicago) as part of Extremal and probabilistic combinatorics we binar\n\n\nAbstract\nWe present a method which provides a unified framewor k for many stability theorems that have been proved in graph and hypergrap h theory. Our main result reduces stability for a large class of hypergrap h problems to the simpler question of checking that a hypergraph $\\math cal H$ with large minimum degree that omits the forbidden structures is v ertex-extendable. This means that if $v$ is a vertex of $\\mathcal H$ and ${\\mathcal H} -v$ is a subgraph of the extremal configuration(s)\, then $ \\mathcal H$ is also a subgraph of the extremal configuration(s). In many cases vertex-extendability is quite easy to verify.\n\nOur method always y ields an Andrásfai-Erdős-Sós type result\, which says if $\\mathcal H$ has large minimum degree\, then it must be a subgraph of one of the extrem al configurations.\n\nThis is joint work with Dhruv Mubayi and Christian R eiher.\n LOCATION:https://researchseminars.org/talk/EPC/70/ END:VEVENT END:VCALENDAR