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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 http://arxiv.org/abs/1312.5336 with Paul Norbury of Melbourne and the Amsterdam School led by Sergey Shadrin.

Joint meeting with Geometry/Topology seminar