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.
|