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Poisson brackets arising in Teichmuller theory and isomonodromic deformations

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Discrete Integrable Systems

In this talk we associate to the Teichmuller space of a disk with n marked points a Garnier system. We show that by clashing poles the Teichmuller space of an annulus with marked points is obtained and give constraints on the monodromy data in order to map the hole to a orbifold point. This construction leads to some interesting Poisson brackets on the geodesic length functions.

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

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