BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Francisco Martin (University of Grenada) DTSTART:20261105T211500Z DTEND:20261105T221500Z DTSTAMP:20261103T081325Z UID:CUNY_GeometricAnalysis/172 DESCRIPTION:Title: When Mean Curvature Flow Breaks: Singularities\, Topology \, and Ilmanen's Conjecture\nby Francisco Martin (University of Grenad a) as part of CUNY Geometric Analysis Seminar\n\nLecture held in GC 6417.\ n\nAbstract\nMean curvature flow is a geometric evolution equation that te nds to smooth surfaces\, but inevitably develops singularities. A fundamen tal question is how the topology of a surface can change as the flow passe s through a singularity. In 1995\, Tom Ilmanen conjectured that genus cann ot increase through such transitions. In this talk\, I will describe recen t joint work with David Hoffman and Brian White that provides counterexamp les to this conjecture. We construct self-similar mean curvature flows pas sing through a conical singularity in which the genus can increase by an a rbitrarily large amount. The construction combines self-shrinkers and self -expanders asymptotic to the same cone\, using ideas from minimal surface theory\, symmetry\, and degree theory.\n LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/172/ END:VEVENT END:VCALENDAR