Abstract

I will start by introducing localization theorems, which are powerful tools in equivariant cohomology that allow one to simplify an integral 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 the 1950s, which is the search for metrics having particularly ‘nice’ curvature properties. In some cases, it is conjectured that the existence of such 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 existence of solutions to geometric PDEs.