A bstract We elaborate on various aspects of our top-down celestial holographic duality
wherein the semiclassical bulk spacetime is a 4d asymptotically flat, self-dual Kähler …

Vertex operator algebra theory is a new area of mathematics. It has been an exciting and
ever-growing subject from the beginning, starting even before R. Borcherds introduced the …

Vertex algebras are algebraic objects that encapsulate the concept of operator product
expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming …

We exhibit an action of Conway's group–the automorphism group of the Leech lattice–on a
distinguished super vertex operator algebra, and we prove that the associated graded trace …

In this paper, we study $ G $-equivariant tensor categories for a finite group $ G $. These
categories were introduced by Turaev under the name of $ G $-crossed categories; the …

Simple, or Kleinian, singularities are classified by Dynkin diagrams of type ADE. Let g be the
corresponding finite-dimensional Lie algebra, and W its Weyl group. The set of g-invariants …

The goal of this paper is to construct infinite-dimensional Lie algebras by using infinite
product identities and to use these Lie algebras to reduce the generalized moonshine …

This thesis deals with a class of integrable field theories called models with twist function.
The main examples of such models are integrable non-linear sigma models, such as the …

We use the unique canonically twisted module over a certain distinguished super vertex
operator algebra—the moonshine module for Conway's group—to attach a weak Jacobi …

We use canonically twisted modules for a certain super vertex operator algebra to construct
the umbral moonshine module for the unique Niemeier lattice that coincides with its root …