q-Difference Equations and p-Curvature
Organizers
Speaker
Time
Thursday, April 3, 2025 12:15 PM - 1:00 PM
Venue
A4-1
Abstract
The concept of $p$-curvature originated in Grothendieck's unpublished work from the 1960s and was subsequently developed further by V. Katz.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.
Speaker Intro
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.