Ahlfors Bers Colloquium

May 19-22, 2005
University of Michigan
Ann Arbor, Michigan

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University of Michigan

Mathematics Department

Organizers
Dick Canary
Juha Heinonen

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Workshop Abstract Detail

Andrew McIntyre Ohio State University

An explicit Belavin-Knizhnik formula Given a compact Riemann surface with hyperbolic metric and a uniformization by a Schottky or quasiFuchsian group, we consider the laplacian acting on sections of powers of the canonical bundle. We write its functional determinant as the modulus squared of a function holomorphic in moduli (representing the "determinant" of the d-bar operator) times a factor depending on a regularized volume of the corresponding infinite volume hyperbolic 3-manifold. We express the holomorphic function as a Selberg zeta type product associated to the 3-manifold, reminiscent of Millson's product for the eta invariant. The result is motivated by conformal field theory; the geometric meaning is still unclear. This is joint work with Leon Takhtajan (SUNY Stony Brook) and Lee-Peng Teo (National Chiao Tung University Taiwan).

Topic: Weil-Petersson Geometry of Teichmuller space