Vertex Algebras in Number Theory, Geometry and Physics

Dr. Sven Möller, TU Hamburg / TU Darmstadt

Vertex algebras describe 2-dimensional conformal field theories in physics. They were introduced in the 1980s to explain mysterious connections between number and representation theory (monstrous moonshine). Recently, they were also shown to capture certain aspects of 4-dimensional superconformal field theories.
In this talk I will describe recent classification results for holomorphic vertex algebras of central charge 24 by means of automorphic forms.
Then, I will sketch classification problems arising in the context of 4-dimensional physics and how they can be tackled using vertex algebras and symplectic geometry.