BIMSA >
Integrable systems blackboard seminar
Statistical mechanics of Coulomb gases as quantum theory on Riemann surfaces
Statistical mechanics of Coulomb gases as quantum theory on Riemann surfaces
Organizers
Speaker
Time
Monday, October 27, 2025 3:20 PM - 4:30 PM
Venue
A7-201
Abstract
Statistical mechanics of 1D multivalent Coulomb gas may be mapped onto non-Hermitian quantum mechanics. We use this example to develop instanton calculus on Riemann surfaces. Borrowing from the formalism developed in the context of Seiberg-Witten duality, we treat momentum and coordinate as complex variables. Constant energy manifolds are given by Riemann surfaces of genus g≥1. The actions along principal cycles on these surfaces obey ODE in the moduli space of the Riemann surface known as Picard-Fuchs equation. We derive and solve Picard-Fuchs equations for Coulomb gases of various charge content. Analysis of monodromies of these solutions around their singular points yields semiclassical spectra as well as instanton effects such as Bloch bandwidth.
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 moving to the United States and 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 fascinated by 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.