Seminar series
Date
Tue, 11 Mar 2025
15:30
15:30
Location
L4
Speaker
Pierre Descombes
Organisation
Imperial College London
Given a quiver (a directed graph) with a potential (a linear combination of cycles), one can study moduli spaces of the associated noncommutative algebra and associate so-called BPS invariants to them. These are interesting because they have a deep link with cluster algebras and provide some kind of noncommutative analogue of DT theory, the study of sheaves on Calabi-Yau 3-folds.
The generating series of BPS invariants for interesting quivers with potentials are in general very wild. However, using the Kontsevich-Soibelman wall-crossing formula, a recursive formula expresses the BPS invariants in terms of so-called attractor invariants, which are expected to be simple in interesting situations. We will discuss them for quivers with potential associated to triangulations of surfaces and quivers with potential giving noncommutative resolutions of CY3 singularities.