Mathematisches Seminar

Herr Alessandro Malusà (QGM Aarhus): "Geometric quantisation and Andersen-Kashaev theory"

23.11.2017 von 16:15 bis 17:45

LMS 4 - Raum 526 - Übungsraum

Abstract:

The SL(2,C)-Chern-Simons theory can be approached in different ways, two of which are geometric quantisation on moduli spaces and Andersen-Kashaev Teichmüller TQFT. Unlike in the case of SU(2), the relation between these different formulations is not yet clear. In the case of a genus one surface, however, the quantum Hilbert spaces coming from these two viewpoints are explicitly isomorphic via the Weil-Gel’fand-Zak transform. In a soon-to-appear work with Andersen, we use geometric quantisation to define quantum operators associated to certain elements of the algebra of regular functions on the moduli space, and use the above-mentioned transform to obtain operators in Teichmüller theory. We then proceed to show an analogous of the AJ-conjecture for these operators and the invariants produced by the TQFT for the first two hyperbolic knots.

Einladender: H. Weiß

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