6:00 pm Thursday, September 25, 2014
Back Porch Seminar: Integrable Systems from Monopoles, Dimers, Loop Groups, and Toric Calabi-Yaus by Harold Williams (UT) in Schedler and Lawn's back porch
We'll talk about an interesting class of integrable systems from many different points of view -- indeed, the fact that we can describe them in so many different ways is one of the main the reasons for thinking they're so interesting. The most classical example of these systems is the "relativistic periodic Toda chain", but don't worry if the name doesn't mean anything to you. Different ways of thinking about the phase spaces of these systems include: spaces of doubly-periodic solutions to the Bogomolny equations (reductions of the self-dual Yang-Mills equations), or subvarieties of loop groups (more precisely, double Bruhat cells of loop groups). These systems can also be built out of noncompact toric CY 3-folds (equivalently, compact toric surfaces) in a suitable sense, or combinatorially from counting perfect matchings on a bipartite graph embedded in T^2. We'll try to at least mention all these points of view, going into more details as time, interest, and the competence of the speaker permit. Submitted by
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