Elliptic representation theory and higher loop Grassmannians

Grant number: DE190101222 | Funding period: 2019 - 2022

Completed

Abstract

This project aims to study symmetries which control geometry and physics of four-dimensional manifolds. Representation theory is the area in pure mathematics which studies symmetries coming from geometry, algebra, and physics. The expected outcome is new families of quantum algebra, their character formulas, and a solution to an infinite-dimensional moduli problem. This project will further deepen the mathematical knowledge of symmetries, and show unexpected new connections between different areas of pure mathematics and mathematical physics.

Related publications (5)

The Cohomological Hall Algebras of a Preprojective Algebra with Symmetrizer

Yaping Yang, Gufang Zhao

2022-03-28

This paper aims at a geometric realization of the Yangian of non-simply laced type in terms of quiver with potentials. For every q..

Representations of the elliptic affine Hecke algebras

G Zhao, C Zhong

2022-02-24

We prove that irreducible representations of the elliptic affine Hecke algebras of Ginzburg, Kapranov, and Vasserot are in one-to-..

Loop Grassmannians of Quivers and Affine Quantum Groups

I Mirković, Y Yang, G Zhao

2022-01-01

We construct for each choice of a quiver Q, a cohomology theory A, and a poset P a “loop Grassmannian” GP(Q, A). This generalizes ..

Wall-crossings and a categorification of K-theory stable bases of the Springer resolution

Changjian Su, Gufang Zhao, Changlong Zhong

2021-11-01

We compare the -theory stable bases of the Springer resolution associated to different affine Weyl alcoves. We prove that (up to r..

Algebraic elliptic cohomology and flops II: SL-cobordism

Marc Levine, Yaping Yang, Gufang Zhao

2021-04-19

In this paper, we study the algebraic Thom spectrum MSL in Voevodsky's motivic stable homotopy category over an arbitrary perfect ..

University of Melbourne Researchers

Gufang Zhao Mathematics and Statistics