Schellekens' VOAs, Generalised Deep Holes and the Very Strange Formula

2020/12/24 木 10:30 - 12:00
Sven Moeller

In this talk I will summarise recent results regarding the
classification of strongly rational, holomorphic VOAs (or CFTs) of
central charge 24 (based on joint works with Jethro van Ekeren, Gerald
Höhn, Ching Hung Lam, Nils Scheithauer and Hiroki Shimakura).
First, we show that there is an abstract bijection (without classifying
either side) between these VOAs and the generalised deep holes of the
Leech lattice VOA. The proof uses a dimension formula obtained by
pairing the VOA character with a vector-valued Eisenstein series and an
averaged version of Kac's Lie theoretic very strange formula. This is a
quantum analogue of the result by Conway, Parker and Sloane (and
Borcherds) that the deep holes of the Leech lattice are in bijection
with the Niemeier lattices.
Then, we explain how this can be used to classify the (exactly 70)
strongly rational, holomorphic VOAs of central charge 24 with non-zero
weight-one space. (The case of zero weight-one space, which includes the
Moonshine module, is more difficult and still open.)

NOTE: This is a zoom seminar.

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Passcode: The order of Weyl group of type $E_7$