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
我的教育始于俄罗斯，在莫斯科物理技术学院学习数学和物理。移居美国后，我于2012年在明尼苏达大学获得博士学位，开始了理论物理学家的研究生涯。起初，我的研究聚焦于超对称规范理论和弦理论的多个方面。然而，自学生时代起，我一直对纯粹抽象数学充满兴趣。约从2017年起，我成为全职数学家。我当前的研究侧重于枚举代数几何、几何表示论与可积系统之间的互动。总的来说，我致力于物理数学的研究，这在当今代表了现代数学的重要组成部分。许多数学家研究的问题来源于弦理论/规范理论。最近，我开始研究数论及其与数学其他分支的联系。如果你是北京地区的博士后或研究生，并有意与我合作，请通过电子邮件联系我。