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Faonte, Hennion, and Kapranov classified higher-dimensional Kac–Moody central extensions using the Jouanolou model for the derived global sections of punctured affine space. In this talk, we use this model to study higher-dimensional chiral algebras. Using higher chiral operations, we construct a distinguished Virasoro central extension in higher dimensions. This is based on joint work with Minghao Wang and Brian Williams, as well as ongoing work with Brian Williams.

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Borcherds' bicharacter construction of vertex algebras was realized by Joyce on the homology of moduli stacks of sheaves. After isolating the appropriate definition of equivariant K-homology, we refine the construction to produce (q,T)-deformed vertex algebras similar to the ones defined by Frenkel-Reshetikhin. These structures govern equivariant wall-crossing of K-theoretic DT invariants. If time permits, I will discuss the Jordan quiver as an illustrative example.

This is based on ongoing joint work with Emile Bouaziz.