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Some analytic problems in two-dimensional conformal field theory

Infinite-Dimensional Geometry December 07, 2013 - December 08, 2013

December 08, 2013 (02:00 PM PST - 02:35 PM PST)
Speaker(s): Eric Schippers (University of Manitoba)
Location: Evans Hall
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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.
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