PIRSA:26030075

Modular Functors from Conformal Blocks of Rational Vertex Operator Algebras

Damiolini, C. (2026). Modular Functors from Conformal Blocks of Rational Vertex Operator Algebras. Perimeter Institute. https://pirsa.org/26030075

Damiolini, Chiara. Modular Functors from Conformal Blocks of Rational Vertex Operator Algebras. Perimeter Institute, Mar. 06, 2026, https://pirsa.org/26030075 

          @misc{ pirsa_PIRSA:26030075,
            doi = {10.48660/26030075},
            url = {https://pirsa.org/26030075},
            author = {Damiolini, Chiara},
            keywords = {Mathematical physics},
            language = {en},
            title = {Modular Functors from Conformal Blocks of Rational Vertex Operator Algebras},
            publisher = {Perimeter Institute},
            year = {2026},
            month = {mar},
            note = {PIRSA:26030075 see, \url{https://pirsa.org}}
          }

Chiara Damiolini The University of Texas at Austin

Talk numberPIRSA:26030075
DOI10.48660/26030075
Collection
Talk Type Scientific Series
Subject

Abstract

Given a vertex operator algebra V, one can define sheaves of conformal blocks on moduli spaces of curves following constructions of Ben-Zvi--Frenkel and Damiolini--Gibney--Tarasca. When V is strongly rational, these sheaves are vector bundles equipped with a projectively flat connection. In this talk, I will explain how these bundles satisfy the compatibility conditions required to form a modular functor. A key consequence of this result is that the category C_V of admissible V-modules is a modular fusion category. This provides a purely algebro-geometric construction of the tensor product on C_V, which is expected to agree with the tensor product defined by Huang and Lepowsky using analytic methods. Time permitting, I will discuss open questions concerning extensions beyond the rational setting. This is joint work with Lukas Woike.