☆ 4.2 Article

Koszul algebras and Donaldson-Thomas invariants

LETTERS IN MATHEMATICAL PHYSICS (2022)

A boson-fermion correspondence in cohomological Donaldson-Thomas theory

Ben Davison

Summary: We introduce a fermionisation procedure that selectively switches the cohomological parity of the BPS Lie algebra. We determine the cohomological Donaldson-Thomas invariants and Borel-Moore homology to generalize previous results.

GLASGOW MATHEMATICAL JOURNAL (2023)

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Some remarks on associated varieties of vertex operator superalgebras

Hao Li

Summary: In this study, several families of vertex operator superalgebras were investigated using a jet (super)scheme point of view. New examples of vertex algebras were provided, which are chiral-quantizations of their C-2-algebras R-V. The examples were derived from various types of vertex algebras, including affine C-l((1))-series, N=1 superconformal algebras, Feigin-Stoyanovsky subspaces, graph vertex algebras, and extended Virasoro algebras. A counterexample to the chiral-quantization property for the N=2 superconformal vertex algebra with central charge 1 was also presented.

EUROPEAN JOURNAL OF MATHEMATICS (2021)

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