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Some analytic problems in two-dimensional conformal field theory
December 08, 2013 (02:00 PM PST - 02:35 PM PST)
Speaker(s):
Eric Schippers (University of Manitoba)
Location:
Evans Hall
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
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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