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Lie Group Quantum Mathematics Seminar

The sewing operation for the determinant line bundle over the Segal moduli space

Eric Schippers, University of Manitoba

Location:  Hill 705
Date & time: Friday, 05 April 2024 at 12:10PM - 1:10PM

Segal considered a determinant line bundle on Riemann surfaces with boundary parametrizations, which plays an important role in two-dimensional conformal field theory. This is the determinant line bundle of the operator pi which takes a holomorphic function on the Riemann surface to the negative Fourier modes of the boundary values of this function. Segal sketched a definition of a sewing operation for this determinant line.

This talk is about some of the interactions between geometry and analysis -- particularly Teichmuller theory -- and the determinant line bundle together with its sewing operation. We also discuss open problems.

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