In recent work on “universal” wall-crossing formulas, Joyce obtains a geometric construction of a vertex algebra structure on the homology groups of moduli stacks parameterizing objects in certain abelian categories. I will review this construction and explain how it may be extended to some sort of equivariant K-homology groups, producing multiplicative and equivariant versions of vertex algebras. These vertex algebras are compatible with cohomological/K-theoretic Hall algebras, of the same moduli stacks, and I will speculate a bit on the role they may play in controlling enumerative invariants, via wall-crossing or otherwise.

This seminar is a hybrid meeting.
Zoom Meeting ID: 867 1000 5800
Passcode: 539591