q-Opers and Bethe Ansatz for Open Spin Chains
演讲者
时间
2026年01月12日 15:20 至 16:30
地点
A7-101
摘要
In in a nutshell, the classical geometric q-Langlands duality can be viewed as a correspondence between the space of (G, q)-opers and the space of solutions of XXZ Bethe Ansatz equations. The latter describe spectra of closed spin chains with twisted periodic boundary conditions and, upon the duality, the twist elements are identified with the q-oper connections on a projective line in a certain gauge. In this work, we initiate the geometric study of Bethe Ansatz equations for spin chains with open boundary conditions. We introduce the space of q-opers whose defining sections are invariant under reflection through the unit circle in a selected gauge. The space of such reflection-invariant q-opers in the presence of certain nondegeneracy conditions is thereby described by the corresponding Bethe Ansatz problem. We compare our findings with the existing results in integrable systems and representation theory. This paper discusses the type-A construction leaving the general case for the upcoming work.
演讲者介绍
My education begain in Russia where I learned math and physics at Moscow Insitute of Physics and Technology. I started my research career as a theoretical physicist after moving to the United States and obtaining my PhD from University of Minnesota in 2012. At first, my research focus was drawn to various aspects of supersymmetric gauge theories and string theory. However, I have always been fascinated by pure abstract mathematics since my student days. Since around 2017 I have been a full time mathematician.
My current research is focused on the interaction between enumerative algebraic geometry, geometric representation theory and integrable systems. In general I work on physical mathematics which nowadays represents a large part of modern math. A significant amount of problems that are studied by mathematicians comes from string/gauge theory. More recently I began to study number theory and how it is connected to other branches of mathematics.
If you are postdoc or a graduate student in Beijing area and you are interested in working with me contact me via email.
My current research is focused on the interaction between enumerative algebraic geometry, geometric representation theory and integrable systems. In general I work on physical mathematics which nowadays represents a large part of modern math. A significant amount of problems that are studied by mathematicians comes from string/gauge theory. More recently I began to study number theory and how it is connected to other branches of mathematics.
If you are postdoc or a graduate student in Beijing area and you are interested in working with me contact me via email.