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Geometric descriptions of the Loewner energy

Presented by: 
Yilin Wang
Tuesday 17th July 2018 - 13:45 to 14:30
INI Seminar Room 1
The Loewner energy of a simple loop on the Riemann sphere is defined to be the Dirichlet energy of its driving function which is reminiscent in the SLE theory. It was shown in a joint work with Steffen Rohde that the definition is independent of the parametrization of the loop, therefore provides a Moebius invariant quantity on free loops which vanishes only on the circles. In this talk, I will present intrinsic interpretations of the Loewner energy (without involving the iteration of conformal distortions given by the Loewner flow), using the zeta-regularizations of determinants of Laplacians and show that the class of finite energy loops coincides with the Weil-Petersson class of the universal Teichmueller space.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons