These days, I'm increasingly interested in approaching vertex algebras using a geometric toolkit.  For now, this means using localisation techniques on sheaves of vertex algebras---a perspective that has proven very fruitful recently. I am also interested in the deformation theory of vertex algebras, mainly working towards classifying chiral quantisations. In my most recent work, I used some of these techniques to prove the inverse Hamiltonian reduction conjecture in type A.

In the past, my research has focused on vertex algebras that arise from four-dimensional physics. These include the so-called chiral algebras of class S: these are vertex algebras labelled by the topological data of a punctured algebraic curve and a simply laced Lie group. In early work, I extended a construction of these vertex algebras, due to Arakawa, to the twisted setting whose existence was predicted by physics.

In Progress:

• On the deformation theory of chiral quantizations joint w. Dylan Butson

• Quasimaps and interfaces to quiver gauge theories joint w. Spencer Tamagni

Preprints:

1. Inverse Hamiltonian reduction for affine W-algebras in type A joint w. Dylan Butson

2. Inverse Hamiltonian reduction in type A and generalised slices in the Affine Grassmannian joint w. Dylan Butson

Publications:

1. The SCFT/VOA correspondence for class S DPhil. Thesis.  

2. Free field realisation and the chiral universal centraliser Ann, Henri Poincare (2023) joint w. Christopher Beem

3. Twisted chiral algebras of class S and mixed Feigin-Frenkel gluing Comm. Math. Phys. (2023) joint w. Christopher Beem