Vertex Algebras

Vertex algebras describe two-dimensional but also higher-dimensional conformal field theories in physics. These play a central role in statistical physics, string theory, and quantum gravity. From a mathematical perspective, vertex algebras are interesting because they connect various fields of research—algebra, number theory, representation theory, and geometry—in exciting ways (e.g., “monstrous moonshine”). In particular, modular forms play an important role in this context.

Our research group focuses on vertex algebras and conformal field theories, as well as objects derived from them, such as automorphic forms, braided tensor categories, infinite-dimensional Lie algebras, and symplectic varieties