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QGM seminar by Louis Ioos (Institut de Mathématiques de Jussieu, Paris)

Title: Geometric quantization of symplectic maps and Witten's asymptotic conjecture

2018.11.27 | Jane Jamshidi

Date Wed 09 Jan
Time 14:15 15:15
Location 1531-113 (Aud. D1)



The process of geometric quantization of a compact symplectic manifold depends on the choice of a complex structure, and a natural way to study this dependence is to consider the spaces of quantum states as a vector bundle over a space of complex structures. This idea is of particular interest in the context of moduli spaces of flat connections over a compact surface and the associated Verlinde bundle over Teichmüller space, for which there exists a canonical projectively flat connection. Parallel transport with respect to this connection allows one to define the Witten-Reshetikhin-Turaev invariant of mapping tori. In this talk, I will discuss the asymptotic expansion of this invariant as the level tends to infinity, and compute its first coefficient. This follows from a general semi-classical study of parallel transport in quantum bundles, via the theory of Berezin-Toeplitz quantization.