Geometric Aspects of Integrable Systems
演讲者
时间
2025年03月24日 12:45 至 13:25
地点
A6-101
线上
Zoom 388 528 9728
(BIMSA)
摘要
The history of integrable systems is a story of deep mathematical structures emerging from physical problems. From classical mechanics to modern quantum theory, integrability continues to inspire new discoveries across mathematical physics.
In the late 20th and early 21st centuries, algebraic geometry and representation theory became fundamental in advancing the study of integrable systems. However, only in recent years has it become possible to fully elucidate the connections and dualities between various integrable systems in purely geometric terms.
In this talk, I will introduce a novel geometric structure—an oper—that captures the phase spaces of a large family of many-body integrable systems as well as the spectra of quantum spin chains. Our approach establishes deep connections with various areas of mathematical physics, including representation theory, cluster algebras, quantum cohomology, and even quantum hydrodynamics.
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。