Wall-crossing for invariants of equivariant 3CY categories (a user guide)

Abstract: In practice, in order to apply the Joyce-style wall-crossing formulas from my previous talk, some control over the wall-crossing term is needed. I will explain how this wall-crossing term, in K-theory, is governed by a certain ``vertex coproduct'' arising from a multiplicative vertex (co)algebra. This vertex coproduct is compatible with K-theoretic Hall operations --- which form positive halves of quantum loop algebras --- whenever they exist. I will present formulas for this coproduct in the easiest cases in 3-fold and 4-fold Donaldson-Thomas theory. Applications include an explicit descendent Donaldson-Thomas/Pandharipande-Thomas vertex correspondence.

algebraic geometryrepresentation theory

Audience: researchers in the topic

Comments: Lecture series: Wall-crossing for invariants of equivariant 3CY categories

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Algebra and Geometry Seminar @ HKUST

Series comments: Algebra and Geometry seminar at the Hong Kong University of Science and Technology (HKUST).

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