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Deep holes in vertex operator algebras

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NCN2 - New connections in number theory and physics

A deep hole of a lattice is a point in the ambient space which has maximal distance to all lattice points. Borcherds showed in 1985 that there is a bijection between the deep holes in the Leech lattice and the Niemeier lattices with roots. Together with the classification of the deep holes in the Leech lattice by Conway, Parker and Sloane this implies the classification of the Niemeier lattices with non-trivial root system. In this talk we explain how the notion of a deep hole can be generalised to holomorphic vertex operator algebras of central charge 24 and how they can be used to classify these vertex operator algebras. This is joint work with Sven Möller.

This talk is part of the Isaac Newton Institute Seminar Series series.

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