The Conformal Packing and Dual Packing Problem
I will formulate the packing and the related dual packing problem for vertex operator algebras in analogy to the classical sphere packing problem and the packing problem for binary codes. The modular bootstrap technique used in quantum gravity allows to obtain explicit numerical upper bounds for the minimal dual conformal weight for fixed central charge c of the vertex operator algebra. By using methods from the solution of the sphere packing problem in dimensions 8 and 24 by Viazovska resp. Cohn et al., I am able to obtain sharp bounds for central charges c=8 and c=24. The two vertex operator algebras realizing these bounds are a vertex operator algebra with the Lie group E_8 as automorphism group and the moonshine module with the Monster simple group as automorphism group.