Thursday 25th of July 2024 - AMS-UMI International Joint Meeting 2024 Palermo 

Special Session B4: New Developments in infinite dimensional Lie algebras, vertex operator algebras and the Monster 

Title: Monstrous Lie algebras as Borcherds algebras

Abstract: We discuss the construction of Carnahan’s non-Fricke monstrous Lie algebras from the point of view of Borcherds algebras. 

Proceedings preprint: https://arxiv.org/abs/2507.17854 

Friday 15th of November 2024 - Lie Group/Quantum Mathematics Seminar (Rutgers University)

Title: Differential equations for twisted intertwining operators among mostly untwisted modules

Abstract: Modules for a vertex operator algebra can be twisted by an automorphism of the vertex operator algebra. Intertwining operators among twisted modules describe how a twisted module can act on another twisted module, analogous to how the vertex operator algebra acts on itself.

It is believed that products of twisted intertwining operators should converge, under suitably nice conditions, as they describe 4-point correlation functions in orbifold conformal field theory. Following Yi-Zhi Huang’s method for proving convergence of products of (untwisted) intertwining operators, we obtain new differential equations for products of certain types of twisted intertwining operators after deriving a new Jacobi identity for them. Physically, the correlation functions we have proved to converge describe how chiral fields from the untwisted sector act on a single chiral twisted sector.

Friday 5th of December 2024 - Lie Group/Quantum Mathematics Seminar (Rutgers University)

Title: C_n-cofinite twisted modules for C_2-cofinite vertex operator algebras

Abstract: There is a well-known finiteness condition for vertex operator algebras and their modules called C_n-cofiniteness. It was shown by Geoffrey Buhl that C_2-cofiniteness of a CFT-type vertex operator algebra is strong enough to guarantee that all of its finitely-generated weak modules are C_n-cofinite for all n > 0. In this talk, we will discuss the extension of Buhl's result to the twisted case, i.e. the orbifold CFT setting. Given a vertex operator algebra V with a general automorphism g of V, we introduce a notion of C_n-cofiniteness for weak g-twisted V-modules. When V is C_2-cofinite and of CFT type, we show that all finitely-generated weak g-twisted V-modules are C_n-cofinite for all n > 0. This talk is based on my work https://arxiv.org/abs/2510.26657.