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The quantum curve for CP^1

QMAP Seminar

Speaker: Motohico Mulase, UC Davis
Location: 2112 MSB
Start time: Thu, Jan 9 2014, 4:10PM

We present a rigorous construction of the quantum curve for the Gromov-Witten theory of CP^1. Mathematically, it is an infinite-order ordinary differential equation that captures *all* information of the Gromov-Witten invariants of CP^1. We'll start with explaining the WKB method for the first quantization of a simple classical mechanical problem. We then introduce the second quantization to go to quantum field theory. The QFT we encounter here turns out to be the Gromov-Witten theory of CP^1. The technical part of the proof requires representation theory of symmetric groups, in particular, the hook-length formula for Young tableaux, in an interesting way. The talk is based on my joint paper with Paul Norbury of Melbourne and the Amsterdam School led by Sergey Shadrin.

Joint meeting with Geometry/Topology seminar