MS Seminar (Mathematics - String Theory)

Speaker: Tudor Padurariu (IMJ-PRG, Sorbonne University)
Title: Quasi-BPS categories for quivers with potentials
Date (JST): Tue, May 28, 2024, 13:30 - 15:00
Place: Seminar Room A
Abstract: For a Calabi-Yau threefold X, one expects to define a Hall algebra using cohomologies of moduli of semistable sheaves on X. This Hall algebra should be a deformation of the universal enveloping algebra of a Lie algebra associated to X, and the dimensions of the graded pieces of this Lie algebra should be the BPS invariants of X, which are some fundamental enumerative invariants.

These Hall algebras are still not defined in full generality. The local case of these Hall algebras should be given by the Hall algebra of a quiver with potential, which has been introduced by Kontsevich-Soibelman. The construction of the associated Lie algebra on BPS cohomology spaces was done by Davison-Meinhardt. For a tripled quiver with potential, the Kontsevich-Soibelman Hall algebra is the same as the preprojective Hall algebra of a quiver (which has been introduced and studied by Schiffmann-Vasserot, Vasserot-Varagnolo, Yang-Zhao), and which is related to Yangians or quantum affine algebras of the quiver.

In this talk, I will explain a categorical version of the BPS cohomology spaces of a quiver with potential, and discuss properties of the categories obtained in the special case of a tripled quiver with potential. This is joint work with Yukinobu Toda.