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SUMMARY:Localization theorems in Kähler geometry - Alexia Corradini\, Ins
 titut Polytechnique de Paris
DTSTART:20220617T150000Z
DTEND:20220617T160000Z
UID:TALK175472@talks.cam.ac.uk
CONTACT:104686
DESCRIPTION:I will start by introducing localization theorems\, which are 
 powerful tools in equivariant cohomology that allow one to simplify an int
 egral over a space with a group action to an integral over its fixed locus
 . I will then describe a very popular problem in Kähler geometry since th
 e 1950s\, which is the search for metrics having particularly 'nice' curva
 ture properties. In some cases\, it is conjectured that the existence of s
 uch metrics is equivalent to some algebro-geometric notion of stability\, 
 and localization can be used to relate these two counterparts\, as well as
  make explicit computations. I will end by talking about my current work\,
  which is to apply this technique to the recent work of Ruadhaí Dervan\, 
 extending this correspondence between algebro-geometric quantities and exi
 stence of solutions to geometric PDEs.
LOCATION:MR13
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