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Quantum curves, Hitchin fibrations, and the Eynard-Orantin theory

QMAP Seminar

Speaker: Motohico Mulase, UC Davis
Location: 2112 MSB
Start time: Thu, Oct 3 2013, 4:10PM

A quantum curve is a magical object. Conjecturally it captures a lot of information of quantum topological invariants. In this talk I will present a new discovery, made in my joint paper with Olivia Dumitrescu of Hanover, that the spectral curves of Hitchin fibrations are quantizable by means of the Eynard-Orantin theory. For the first time we present the Eynard-Orantin theory on an arbitrary base curve, and show that the theory is designed to define a canonical generator of a D-module on the curve. Despite the scary terminologies, the talk will be given in an elementary language. The aim of the talk is to show the amazing scope of the new discovery that relates a B-model topological string theory, algebraic geometry of Hitchin fibrations, classical Riemann surface theory, and a glimpse into quantum knot invariants and number theory.