Workshop Infinite-Dimensional Geometry

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Dec 08, 2013
Sunday

02:00 PM - 02:35 PM		Some analytic problems in two-dimensional conformal field theory Eric Schippers (University of Manitoba)
Location Evans Hall Video -- Abstract A central object of two-dimensional conformal field theory is the Friedan/Shenker/Vafa moduli space of Riemann surfaces with boundary parameterizations. Radnell and I showed that this moduli space can be identified with the (infinite dimensional) Teichmuller space of bordered surfaces up to a properly discontinuous fixed-point-free group action. In this talk I will give an overview of joint results with Radnell and Staubach, in which we use this correspondence to solve certain analytic problems in the construction of CFT. I will also discuss the relation of these problems to a refinement of Teichmuller space on which the Weil-Petersson metric converges. In particular, we constructed a Teichmuller space of genus g with n boundary curves which is a Hilbert manifold and has a convergent Weil-Petersson metric. This generalizes results of Takhtajan, Teo, Hui, Cui and others for the case of the disc. Supplements -- Show Detail