BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gergely Ambrus (Alfréd Rényi Institute of Mathematics and Univer sity of Szeged) DTSTART:20210920T190000Z DTEND:20210920T200000Z DTSTAMP:20260423T035957Z UID:paw/32 DESCRIPTION:Title: Str ongly Convex Chains\nby Gergely Ambrus (Alfréd Rényi Institute of Ma thematics and University of Szeged) as part of Probability and Analysis We binar\n\n\nAbstract\nIt is a classical question to study the length of the longest monotone increasing subsequence in a random permutation on n elem ents\, which has been studied for over half a century. From the geometric viewpoint\, the question asks for the maximal number of points in a random sample of n uniform\, independent points in a unit square which form an i ncreasing chain. Based on this geometric intuition\, one may study the max imal number of points (called the length) which form a convex chain\, alon g with two fixed vertices of the unit square. In a joint work with Imre B árány\, we determined the asymptotic order of magnitude of the length of the longest convex chain\, proved strong concentration estimates and a li mit shape result. In a recent work\, I studied the analogous question for higher order convexity\, and managed to determine the expected length in t his case as well (which turns out to be very aesthetic)\, along with conce ntration properties. In the talk I will give a survey of these results and present several open questions and further research directions.\n LOCATION:https://researchseminars.org/talk/paw/32/ END:VEVENT END:VCALENDAR