Curve Counting, Geometric Representation Theory, and Quantum Integrable Systems

Date
2017/11/13 Mon 16:30 - 18:30
2017/11/15 Wed 14:45 - 16:45
2017/11/16 Thu 14:45 - 16:45
2017/11/20 Mon 16:30 - 18:30
2017/11/21 Tue 14:45 - 16:45
Room
3号館127大会議室
Speaker
Andrei Okounkov
Affiliation
Kyoto University / Columbia University
Abstract

My goal in these lectures will be to explain, focusing on the simplest example of cotangent bundles of Grassmannian, how counting rational curves in certain algebraic varieties is related to several branches of mathematics pioneered and developed here in Kyoto, especially to the quantum group analysis of integrable spin chains and to the geometric realization of quantum groups provided by the Nakajima varieties.

This connection was discovered by Nekrasov and Shatashvili and the example of the Grassmannians is really the most basic example in which the theory can be fully explained. If time permits, I will try to describe the general contours of the theory, as we see them today.

[NOTE] This series of lectures will be video-recorded and made available online. Please note that anyone in the front rows of the room can be captured by a video camera.

Poster (pdf)