New algebraic structures from Calabi-Yau three
Organizers
Speaker
Time
Thursday, January 22, 2026 3:00 PM - 4:00 PM
Venue
A6-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
Cohomological Hall algebras allow us to understand coherent sheaves on a CY3 - and similar categories - by turning them into objects in representation theory.
I will explain this story, first due to Kontsevich and Soibelman, as well as the physicists' version of it in terms of categories of line operators for QFTs.
The main part of this talk describes recent work (with S. Jindal, S. Kaubrys, also with P. Descombes) in constructing these physics-predicted "quantum group"-like structures on cohomological Hall algebras and their category of modules. I will finish by explaining why this is useful in representation theory.
I will try to make this talk accessible to geometers not familiar with representation theory.
I will explain this story, first due to Kontsevich and Soibelman, as well as the physicists' version of it in terms of categories of line operators for QFTs.
The main part of this talk describes recent work (with S. Jindal, S. Kaubrys, also with P. Descombes) in constructing these physics-predicted "quantum group"-like structures on cohomological Hall algebras and their category of modules. I will finish by explaining why this is useful in representation theory.
I will try to make this talk accessible to geometers not familiar with representation theory.
Speaker Intro
Alexei Latyntsev is a mathematician specializing in algebraic geometry, geometric representation theory, and enumerative invariants. He completed a first-class BA and a distinction MA in Mathematics at Trinity College, Cambridge, followed by a PhD at the University of Oxford. He has extensive teaching and mentoring experience, having served as a lecturer, teaching assistant, and tutor at the University of Oxford and SDU, covering a wide range of advanced mathematics courses. He is also an active organizer of research seminars, including the Oxford Physics and Geometry Seminar and the online Factorisation Algebras seminar.