BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dan Kráľ (Masaryk University) DTSTART:20211220T140000Z DTEND:20211220T150000Z DTSTAMP:20260423T035412Z UID:EPC/80 DESCRIPTION:Title: Qua sirandom graphs\, permutations and Latin squares\nby Dan Kráľ (Masar yk University) as part of Extremal and probabilistic combinatorics webinar \n\n\nAbstract\nA combinatorial structure is said to be quasirandom if it resembles a random structure in a certain robust sense. The notion of quas irandom graphs\, developed in the work of Rödl\, Thomason\, Chung\, Graha m and Wilson in 1980s\, is particularly robust as several different proper ties of truly random graphs\, e.g.\, subgraph density\, edge distribution and spectral properties\, are satisfied by a large graph if and only if on e of them is. A closely related notion is the notion of common graphs\, wh ich are graphs whose number of monochromatic copies is minimized by the (q uasi)random coloring of a host complete graph.\n\n \nWe will disc uss quasirandom properties of permutations and Latin squares\, and present several recent results obtained using analytic tools of the theory of com binatorial limits. We will also present some recent results on common and locally common graphs\, in particular\, we show that there exists common c onnected graphs with arbitrary large chromatic number\, whose existence wa s an open problem for more than 20 years.\n\n\nThe talk is based on result s obtained with different groups of collaborators\, including Timothy F. N . Chan\, Jacob W. Cooper\, Robert Hancock\, Matjaž Krnc\, Ander Lamaison\ , Samuel Mohr\, Jonathan A. Noel\, Sergey Norin\, Yanitsa Pehova\, Oleg Pi khurko\, Maryam Sharifzadeh\, Jan Volec and Fan \nWei.\n LOCATION:https://researchseminars.org/talk/EPC/80/ END:VEVENT END:VCALENDAR