BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Theodora Bourni (University of Tennessee\, Knoxville) DTSTART:20210831T170000Z DTEND:20210831T180000Z DTSTAMP:20260423T035037Z UID:OSGA/79 DESCRIPTION:Title: An cient polygonal pancakes.\nby Theodora Bourni (University of Tennessee \, Knoxville) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract \nMean curvature flow (MCF) is the gradient flow of the area functional\; it moves the surface in the direction of steepest decrease of area. An im portant motivation for the study of MCF comes from its potential geometric applications\, such as classification theorems and geometric inequalities . MCF develops ``singularities'' (curvature blow-up)\, which obstruct the flow from existing for all times and therefore understanding these high cu rvature regions is of great interest. This is done by studying ancient so lutions\, solutions that have existed for all times in the past\, and whic h model singularities. In this talk we will discuss their importance and w ays of constructing and classifying such solutions. In particular\, we wil l focus on ``collapsed'' solutions and construct\, in all dimensions $n\\g e 2$\, a large family of new examples\, including both symmetric and asymm etric examples\, as well as many eternal examples that do not evolve by tr anslation. Moreover\, we will show that collapsed solutions decompose ``b ackwards in time'' into a canonical configuration of Grim hyperplanes whic h satisfies certain necessary conditions. This is joint work with Mat Lang ford and Giuseppe Tinaglia.\n LOCATION:https://researchseminars.org/talk/OSGA/79/ END:VEVENT END:VCALENDAR