BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Benny Sudakov (ETH Zürich) DTSTART:20201130T140000Z DTEND:20201130T150000Z DTSTAMP:20260423T035411Z UID:EPC/36 DESCRIPTION:Title: Thr ee problems on 3-chromatic intersecting hypergraphs\nby Benny Sudakov (ETH Zürich) as part of Extremal and probabilistic combinatorics webinar\ n\n\nAbstract\nThe study of non-2-colorable hypergraphs has a long history going back almost 60 years to the famous problem of Erdos and Hajnal\, wh o asked for the minimum number of edges in such a k-uniform hypergraph. In 1973 Erdos and Lovasz further asked what happens if in addition to non-2- colorability one requires the hypergraph to be intersecting. Their seminal paper\, which introduced the local lemma\, contains three intriguing prob lems on the properties of 3-chromatic intersecting hypergraphs. Despite th ese problems being reiterated several times over the years by Erdos and ot her researchers\, remarkably they withstood any progress up until now. In this talk\, we prove that in any 3-chromatic intersecting k-uniform hyperg raph there are at least $k^{1/2-o(1)}$ different intersection sizes among pairs of edges. This proves a conjecture of Erdos and Lovasz in a strong f orm and substantially improves their previously best bound of at least 3 d ifferent intersection sizes.\n\nJoint work with M. Bucic and S. Glock\n LOCATION:https://researchseminars.org/talk/EPC/36/ END:VEVENT END:VCALENDAR