The loop-nilpotent cohomological Hall algebra and integral forms of YangiansOberseminar Darstellungstheorie

by Shivang Jindal (EPFL Lausanne)

Wednesday Nov 4, 2026, 10:00 AM → 12:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Seminar Room (Max Planck Institute for Mathematics)

Given a quiver with potential, Kontsevich and Soibelman defined its cohomological Hall algebra (CoHA) as a mathematical model for the algebra of BPS states. Since then, CoHAs have been found to have connections with several areas of mathematics, including cohomological Donaldson–Thomas theory, quantum groups, non-abelian Hodge theory, and cluster algebras. In certain cases, dimensional reduction identifies the CoHA with a preprojective CoHA, an algebra that appears naturally in the Schiffmann–Vasserot proof of the AGT conjecture and in the study of Nakajima quiver varieties.

In this talk, I will introduce an algebra combining features of these constructions, which we call the loop nilpotent CoHA. will describe this algebra as a subalgebra of a shuffle algebra, characterised by certain integral wheel conditions. I will then explain how, for quivers of finite type, this algebra can be identified with the positive half of the Drinfeld–Gavarini dual of the Yangian. We will also see how this description leads to a characterisation of the Kac polynomials of a quiver in terms of dimensions of spaces of symmetric polynomials satisfying explicit degree and divisibility conditions. If time permits, I will explain how the loop-nilpotent CoHA admits a surjective homomorphism onto the positive half of the corresponding quantized Coulomb branch algebra.

This talk is based on joint work with Andrei Neguț.