Equivariant wall-crossing seminar: Equivariant homology theories, T-deformed vertex algebras, and equivariant wall-crossing

Speaker: Arkadij Bojko

Abstract: Over the last few sessions, we have explored Joyce’s wall-crossing framework and his construction of vertex algebras from multiple different perspectives. However, we have not yet discussed how it can be applied to study equivariant enumerative invariants. To do this, we first need to understand a prototypical, simple example. Building upon it, I will isolate the appropriate definition of equivariant generalized homology theories for stacks. This construction produces adic-complete modules. In homology, this provides precisely the framework for T-deformed vertex algebras, which I previously termed additive deformations. These refine Haisheng Li’s axioms by controlling the poles and can often be computed explicitly. Using the entire package, we will finish by studying Hilbert schemes of points on affine spaces.

Time: 20:00-22:00, 2026-02-26

Location: R1210, SIMIS
Jitsi link: https://meet.jit.si/moderated/153fb48195a4318e3f1199e421666859d52ebad7351a6a296ac29332115c0851