# Mathematics Colloquia and Seminars

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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