The sewing-factorization theorem for $C_2$-cofinite VOAsConfirmed

by Hao Zhang (Tsinghua University)

Thursday Mar 20, 2025, 11:00 a.m. → 12:30 p.m. America/Toronto

PI/4-400 - Space Room (Perimeter Institute for Theoretical Physics)

In this talk, I will present a sewing-factorization theorem for conformal blocks in arbitrary genus associated to a (possibly nonrational) $C_2$-cofinite VOA $V$. This result gives a higher genus analog of Huang-Lepowsky-Zhang's tensor product theory. Moreover, I will explain the relation between our result and pseudotraces, and confirm some of the conjectures by Gainuditnov-Runkel. The relationship between our result and coends will also be discussed. The talk is based on an ongoing project (arXiv: 2305.10180, 2411.07707) joint with Bin Gui.