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Moduli spaces and elliptic difference equations

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If you have a question about this talk, please contact Mustapha Amrani.

Discrete Integrable Systems

Sakai’s elliptic Painlev equation is constructed via the geometry of certain rational algebraic surfaces. I’ll discuss joint work with Arinkin and Borodin in which we interpret Sakai’s surfaces as moduli spaces of second-order linear elliptic difference equations (and related objects), such that the elliptic Painlev equation itself acts via isomonodromy transformations. The construction also lends itself to higher-order problems, and/or problems with more complicated singularity structure; I’ll discuss what is known about the corresponding higher-dimensional moduli spaces.

This talk is part of the Isaac Newton Institute Seminar Series series.

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