Research

Papers

• Toroidal analogues of the Grothendieck-Springer map Available on arixv at https://arxiv.org/abs/2311.00355

• Elliptic surfaces and toroidal superalgebras Available on arxiv at https://arxiv.org/abs/2311.00349

• Affinizations of Lorentzian Kac-Moody Algebras and Hilbert Schemes of Points on K3 Surfaces Available on arxiv at https://arxiv.org/abs/2007.04953
• Moonshine for all finite groups (with Xavier Gonzalez, Neekon Vafa, and Roger Van Peski)
  Research in the Mathematical Sciences 5.1 (2018), 14.

Software

The following SageMath code and associated Jupyter notebooks were mostly not designed for public use and come with no guarantee of correctness. Nevertheless they may prove useful to somebody.

• Vertex algebras contains code and notebooks allowing for the calculation of OPEs in vertex (super)algebras. It is even clever enough to handle terms from the non-singular part of OPEs which are useful for a number of applications.

• Lie algebra methods contains methods for even lattice vertex operator algebras and Kac-Moody algebras. E.g. one may find a basis for a given root space of a Kac-Moody algebra in terms of Chevalley generators.

• Quiver methods contains methods for doing calculations with quiver varieties and quiver representations. E.g. computing the stratifications of quiver varieties for non-generic stability parameter.

• n-dimensional partitions allows one to do some computations with n-dimensional partitions extending the plane partition calculations already available in sage.