PIRSA:25040122

Video URL

https://pirsa.org/25040122

Quantum groups from cohomological Donaldson-Thomas theory

Jindal, S. (2025). Quantum groups from cohomological Donaldson-Thomas theory. Perimeter Institute for Theoretical Physics. https://pirsa.org/25040122

Jindal, Shivang. Quantum groups from cohomological Donaldson-Thomas theory. Perimeter Institute for Theoretical Physics, Apr. 17, 2025, https://pirsa.org/25040122 

          @misc{ scivideos_PIRSA:25040122,
            doi = {10.48660/25040122},
            url = {https://pirsa.org/25040122},
            author = {Jindal, Shivang},
            keywords = {Mathematical physics},
            language = {en},
            title = {Quantum groups from cohomological Donaldson-Thomas theory},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2025},
            month = {apr},
            note = {PIRSA:25040122 see, \url{https://scivideos.org/index.php/pirsa/25040122}}
          }

Shivang Jindal

Talk numberPIRSA:25040122
DOI10.48660/25040122
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

In 2010, Kontsevich and Soibelman defined Cohomological Hall Algebras for quivers and potential as a mathematical construction of the algebra of BPS states. These algebras are modeled on the cohomology of vanishing cycles, which makes these algebras particularly hard to study but often result in interesting algebraic structures. A deformation of a particular case of them gives rise to a positive half of Maulik-Okounkov Yangians. The goal of my talk is to give an introduction to these ideas and explain how for the case of tripled cyclic quiver with canonical cubic potential, this algebra turns out to be one-half of the universal enveloping algebra of the Lie algebra of matrix differential operators on the torus, while its deformation turn out be one half of an explicit integral form of the Affine Yangian of gl(n).