Gopakumar–Vafa Invariants for cAn Singularities via Contraction Algebras
Organizers
Speaker
Hao Zhang
Time
Thursday, March 12, 2026 10:00 AM - 11:00 AM
Venue
A6-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
Gopakumar–Vafa (GV) invariants are often difficult to compute directly from moduli spaces. In the setting of crepant resolutions of compound Du Val singularities, Toda’s formula relates GV invariants to noncommutative deformation theory via the contraction algebra.
In this talk, I explain how to compute and organise GV-type invariants for crepant partial resolutions of cAn singularities using contraction algebras and quivers with potential. I introduce generalised GV invariants for crepant partial resolutions, discuss an extension of Toda’s formula in this setting, and show that these invariants are determined by the isomorphism class of the contraction algebra. Finally, I describe two further structural results: a natural filtration on the parameter space of contraction algebras (or Type A potentials) for cAn crepant resolutions, and explicit numerical constraints on the possible tuples of GV invariants.
In this talk, I explain how to compute and organise GV-type invariants for crepant partial resolutions of cAn singularities using contraction algebras and quivers with potential. I introduce generalised GV invariants for crepant partial resolutions, discuss an extension of Toda’s formula in this setting, and show that these invariants are determined by the isomorphism class of the contraction algebra. Finally, I describe two further structural results: a natural filtration on the parameter space of contraction algebras (or Type A potentials) for cAn crepant resolutions, and explicit numerical constraints on the possible tuples of GV invariants.