Back to Algebraic Geometry Seminar: Spring 2015
Algebraic Geometry Seminar
Date: Tuesday, Apr 28, 2015
Time: 3:30PM - 4:30PM
Location: LCB 215
Motohico Mulase
UC Davis
Title |
Quantum curves and topological recursion |
Abstract |
Quantum curves are conceived in physics as a result of geometric quantization of the SL(2) character variety of a knot group, which is an infinite-order differential operator that characterizes the colored Jones polynomial. The physics speculation relates the character variety, which is an algebraic curve defined over the integer ring, and the colored Jones polynomial through the topological recursion of Eynard, Orantin, and their collaborators. A mathematical relation between the topological recursion and quantum curves has been discovered in my joint work with Olivia Dumitrescu in the context of Hitchin’s theory of Higgs bundles on a curve. Although it has nothing to do with knot polynomials, the geometric structure becomes clear i this theory. This talk surveys recent mathematical developments around quantum curves and topological recursion, both concrete examples and an algebraic geometry theory of the notion. |
Algebraic Geometry