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
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。