q-Difference Equations and p-Curvature
演讲者
时间
2025年04月03日 12:15 至 13:00
地点
A4-1
摘要
The concept of $p$-curvature originated in Grothendieck's unpublished work from the 1960s and was subsequently developed further by V. Katz. The $p$-curvature plays an important role in the theory of ordinary differential equations (ODEs) as well as holonomic PDEs, establishing a connection between the existence of algebraic fundamental solutions and their behavior under reduction modulo a prime $p$.
In this talk, I will describe how the $p$-curvature can be obtained from a reduction of a quantum difference equation on a Nakajima quiver variety $X$ over the field of finite characteristic. Using a Frobenius map, I will show how to calculate the spectrum of this $p$-curvature.
In this talk, I will describe how the $p$-curvature can be obtained from a reduction of a quantum difference equation on a Nakajima quiver variety $X$ over the field of finite characteristic. Using a Frobenius map, I will show how to calculate the spectrum of this $p$-curvature.
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。