Multiplicative vertex algebras and wall-crossing in equivariant K-theory

Henry Liu (University of Oxford)

Wednesday 30th November, 2022 16:00-17:00 Maths 311B


I will explain how a recent “universal wall-crossing”
framework of Joyce works in equivariant K-theory, which I view as a
multiplicative refinement of equivariant cohomology. Enumerative
invariants, possibly of strictly semistable objects living on the
walls, are controlled by a certain (multiplicative version of) vertex
algebra structure on the K-homology groups of the ambient stack. In
very special settings like refined Vafa-Witten theory, one can obtain
some explicit formulas. For moduli stacks of quiver representations,
this geometric vertex algebra is dual in some sense to the
quantum loop algebras that act on the K-theory of stable loci.

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