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SUMMARY:Theodora Bourni (Tennessee)
DTSTART:20210126T134500Z
DTEND:20210126T144500Z
DTSTAMP:20260423T005658Z
UID:BOWL/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BOWL/11/">An
 cient solutions to mean curvature flow</a>\nby Theodora Bourni (Tennessee)
  as part of B.O.W.L Geometry Seminar\n\n\nAbstract\nMean curvature flow (M
 CF) is the gradient flow of the area functional\; it moves the surface in 
 the direction of steepest decrease of area.  An important motivation for t
 he study of MCF comes from its potential geometric applications\, such as 
 classification theorems and geometric inequalities. MCF develops “singul
 arities” (curvature blow-up)\, which obstruct the flow from existing for
  all times and therefore understanding these high curvature regions is of 
 great interest.  This is done by studying ancient solutions\, solutions th
 at have existed for all times in the past\, and which model singularities.
  In this talk we will discuss their importance and ways of constructing an
 d classifying such solutions. In particular\, we will focus on “collapse
 d” solutions and construct\, in all dimensions $n\\geq 2$\, a large fami
 ly of new examples\, including both symmetric and asymmetric examples\, as
  well as many eternal examples that do not evolve by translation. Moreover
 \,  we will show that collapsed solutions decompose “backwards in time
 ” into a canonical configuration of Grim hyperplanes which satisfies cer
 tain necessary conditions. This is joint work with Mat Langford and Giusep
 pe Tinaglia.\n
LOCATION:https://researchseminars.org/talk/BOWL/11/
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