Bernd Siebert
Schriftzug: Fachbereich Mathematik 
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Research Seminar: Complex Geometry

20.11.2015 Gaetan Borot (MPI Bonn)

Topological recursion and wave functions

Abstract: I will describe the notion of loop equations, and their solution by a topological recursion. The initial data for this recursion is a spectral curve, and the output encodes (in particular) information on variation of complex structures on this curve. Out of the topological recursion, one can construct a "wave function", which in the simplest case is a formal asymptotic series for a section of a certain line bundle over the spectral curve (which should be thought of as a lagrangian in a symplectic surface). I will explain known properties and conjectures about the wave function. I shall illustrate its potential relevance by a conjecture concerning the quantization of the SL_2(C) character variety of 1-cusped 3-manifolds. This is based on joint work with Bertrand Eynard.


 
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