A-type Quiver Varieties and ADHM Moduli Spaces
演讲者
时间
2025年02月28日 13:00 至 14:30
地点
A3-4-301
线上
Zoom 242 742 6089
(BIMSA)
摘要
We study quantum geometry of Nakajima quiver varieties of two different types - framed A-type quivers and ADHM quivers. While these spaces look completely different we find a surprising connection between equivariant K-theories thereof with a nontrivial match between their equivariant parameters. In particular, we demonstrate that quantum equivariant K-theory of An quiver varieties in a certain n→∞ limit reproduces equivariant K-theory of the Hilbert scheme of points on C2. We analyze the correspondence from the point of view of enumerative geometry, representation theory and integrable systems. We also propose a conjecture which relates spectra of quantum multiplication operators in K-theory of the ADHM moduli spaces with the solution of the elliptic Ruijsenaars-Schneider model.
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.