Research

Keywords:

Representation theory
Geometry
Quantum field theory (QFT)

Much of my research so far has regarded 3d mirror symmetry, a duality between topological twists of 3d N=4 QFTs. In particular, I have worked on understanding the symplectic duality between the Higgs and Coulomb branches of such a theory. For a mathematical introduction to the subject see this article.

So far I have studied this phenomenon using a mix of representation theory and geometry involving algebraic objects such as vertex algebras and KLR algebras.

During my MPhil, I constructed so-called “staggered” modules for the $W_3$ -algebra. These modules are both reducible and indecomposable and appear in the study of logarithmic conformal field theory.

I am generally interested in topics involving:

Topological & conformal QFT
Non-semisimple & infinite-dimensional representation theory
Algebraic & symplectic geometry
Categorification
Chiral, vertex & factorization algebras
3d mirror symmetry & holography

Papers:

$L_1(\mathfrak{psl}_{n|n})$ from BRST reductions, associated varieties and nilpotent orbits, arXiv:2409.13028, with Andrea Ferrari.
Tilting generator for $T^*\mathrm{Gr}(2,4)$ , arXiv:2409.01379, with Ben Webster.