Algebra Seminar: A Geometric Classification of the Holomorphic Vertex Operator Algebras of Central Charge 24

Monday, October 31, 2022 4:30pm to 5:20pm

Speaker: Sven Möller (University of Hamburg, Germany)

Abstract: Borcherds showed that there is a bijection between the deep holes of the Leech lattice and the Niemeier lattices with non-trivial root system. This allows a geometric classification of these lattices (by means of certain Dynkin diagrams called hole diagrams). Using modular forms we recently established an analogous result for the holomorphic vertex operator algebras of central charge 24 with non-trivial weight-1 space. They are in bijection with the generalised deep holes of the Leech lattice vertex operator algebra. In this talk I will present a geometric classification of these vertex operator algebras based on this result (by means of certain generalised hole diagrams). This is joint work with Nils Scheithauer.

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