BIMSA > BIMSA Integrable Systems Seminar Elliptic complex reflection groups and Seiberg–Witten integrable systems
Elliptic complex reflection groups and Seiberg–Witten integrable systems
Organizers
Nicolai Reshetikhin , Ivan Sechin , Andrey Tsiganov
Speaker
Oleg Chalykh
Time
Tuesday, April 16, 2024 5:20 PM - 6:20 PM
Venue
A6-101
Online
Zoom 873 9209 0711 (BIMSA)
Abstract
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.
Speaker Intro
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.