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BIMSA Integrable Systems Seminar
Elliptic complex reflection groups and Seiberg–Witten integrable systems
Elliptic complex reflection groups and Seiberg–Witten integrable systems
演讲者
Oleg Chalykh
时间
2024年04月16日 17:20 至 18:20
地点
A6-101
线上
Zoom 873 9209 0711
(BIMSA)
摘要
For any abelian variety $X$ with an action of a finite complex reflection group $W$, Etingof, Felder, Ma and Veselov constructed a family of integrable systems on $T^*X$. When $X$ is a product of $n$ copies of an elliptic curve $E$ and $W=S_n$, this reproduces the usual elliptic Calogero-Moser system. Recently, together with Philip Argyres (Cincinnati) and Yongchao Lü (KIAS), we proposed that many of these integrable systems at the classical level can be interpreted as Seiberg-Witten integrable systems of certain supersymmetric quantum field theories. I will describe our progress in understanding this connection for the case $X=E^n$ where $E$ is an elliptic curve with the symmetry group $Z_m$ (of order $m=2,3,4,6$), and $W$ is the wreath product of $Z_m$ and $S_n$. I will mostly talk about $n=1$ case, which is already rather interesting. Based on: arXiv 2309.12760.
演讲者介绍
Oleg Chalykh obtained his PhD from Moscow State University in 1992, after which he worked at the Moscow State University and Kolmogorov School, then held visiting research positions at Loughborough University (UK) and Cornell University (USA) before moving to the University of Leeds (UK) in 2004 where he has been since. His interests include integrable systems, mathematical physics, and representation theory.