Vector-valued Eisenstein series and classification of holomorphic vertex operator algebras

Abstract: Vertex operator algebras (VOAs) axiomatise 2-dim. conformal field theoories in physics and are at the centre of remarkable conections between representation and number theory (e.g. Monstrous Moonshine).

Indeed, through their characters/graded dimensions, VOAs are intimately connected with various types of modular forms.

In this work we study identities for holomorphic VOAs of central charge 24 based on a pairing argument with vector-valued Eisenstein series of weight 2. The thus obtained dimension formulae are then used to prove a classification result for these VOAs, which had been open for thirty years.

number theory

Audience: researchers in the topic

Japan Europe Number Theory Exchange Seminar

Series comments: The purpose of the Japan Europe Number Theory Exchange Seminar is to give a opportunity for researchers in Japan and Europe to exchange their research projects by giving short talks (30 min). The target audience are researchers of any level in the area of number theory.

Start for Fall 2021: 26th October