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BIMSA Lecture
Coproducts on critical cohomological Hall algebras - what structure is there on module categories of affine quantum groups?
Coproducts on critical cohomological Hall algebras - what structure is there on module categories of affine quantum groups?
Organizer
Speaker
Alyosha Latyntsev
Time
Friday, June 13, 2025 11:00 AM - 12:00 PM
Venue
A3-3-301
Online
Zoom 482 240 1589
(BIMSA)
Abstract
Many of the algebraic objects which launched the study of geometric representation theory in the 80s and 90s, like Drinfeld's Yangians and quantum groups, it turns out are the cohomologies of certain 3-Calabi-Yau moduli stacks (cohomological Hall algebras). Physically, categories C of CoHA-modules are line operators for string theory on a 3CY manifold. We will review the (limited) extent to which this has been made rigorous, and what structures on C this predicts.
The bulk of the talk is about constructing the physics-predicted algebraic structures on C, or equivalently on the CoHA. We construct a coproduct on the CoHA locally in the 3CY moduli stack M, and discuss how it patches. This coproduct is coloured by cohomology generators of M, which we show induces a vertex coproduct, which we show recovers Drinfeld's original coproduct. We give a conceptual definition of extending general CoHAs.
(Joint with S. Kaubrys and S. Jindal)
The bulk of the talk is about constructing the physics-predicted algebraic structures on C, or equivalently on the CoHA. We construct a coproduct on the CoHA locally in the 3CY moduli stack M, and discuss how it patches. This coproduct is coloured by cohomology generators of M, which we show induces a vertex coproduct, which we show recovers Drinfeld's original coproduct. We give a conceptual definition of extending general CoHAs.
(Joint with S. Kaubrys and S. Jindal)