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Title:
Poisson Geometry, Crystals, and Integrable Systems
Speaker:
Abstract:
I will introduce the notion of a Poisson variety with potential, and its partial tropicalization. These objects are related to the geometric crystals of Berenstein and Kazhdan, and help us understand certain Poisson-Lie groups in terms of their representation theory. An ongoing project is to use this technology to build a Gelfand-Cetlin completely integrable system on the dual of any compact Lie algebra. This involves viewing the partial tropicalization as a limit of a scaling transformation using the Ginzburg-Weinstein isomorphism.
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