On the Quantum K-theory of Quiver Varieties at Roots of Unity
演讲者
时间
2024年12月05日 15:00 至 16:00
地点
A6-101
线上
Zoom 638 227 8222
(BIMSA)
摘要
In the framework of equivariant quantum K-theory of Nakajima quiver varieties we construct a q-analog of a Frobenius intertwiner between $\mathbb{Z}/p\mathbb{Z}$-equivariant quantum K-theory and the standard conventional quantum K-theory. We prove that this operator has no poles at primitive complex $p$-th roots of unity in the curve counting parameter $q$. As a byproduct, we show that the eigenvalues of the iterated product of quantum difference operators by quantum bundles $\mathcal{L}$ of quiver variety $X$
evaluated at roots of unity are governed by Bethe equations for $X$ with all variables substituted by their $p$-th powers. In the cohomological limit, the above iterated product is conjectured to reduce to the p-curvature of the quantum connection for prime $p$.
evaluated at roots of unity are governed by Bethe equations for $X$ with all variables substituted by their $p$-th powers. In the cohomological limit, the above iterated product is conjectured to reduce to the p-curvature of the quantum connection for prime $p$.
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 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 drawn to 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.