Act globally, compute locally: group actions, fixed points, and localization

Act globally, compute locally: group actions, fixed points, and localization

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Tara Holm , Cornell and the IAS
Fine Hall 314

Localization is a topological technique that allows us to make global equivariant computations in terms of local data at the fixed points. For example, we may compute a global integral by summing integrals at each of the fixed points. Or, if we know that the global integral is zero, we conclude that the sum of the local integrals is zero. This often turns topological questions into combinatorial ones and vice versa. I will give an overview of how this technique arises in symplectic geometry, and some details about some recent projects in this area.