Fall, 2020
- Speaker Bin Gui, Rutgers University
- Title Convergence of sewing conformal blocks
- Time 11/6/2020, Friday, 12:00 (Eastern Time)
- Location Zoom link above
- Abstract Conformal blocks (i.e. chiral correlation functions) are central objects of chiral CFT. Given a VOA V and a compact Riemann surface C with marked points, one can define conformal blocks to be linear functionals on tensor products of V-modules satisfying certain (co)invariance properties related to V and C. For instance, the vertex operator of a VOA V, or more generally, an intertwining operator of V, is a conformal block associated to V and the genus 0 Riemann surface with 3 marked points. Taking contractions/q-traces is a main way of constructing higher genus conformal blocks from low genus ones, and it has been conjectured for a long time that the contractions always converge. In this talk, I will report recent work on a solution of this conjecture.
- Speaker Thomas Gemünden, ETH Zürich
- Title Non-abelian orbifold theory and holomorphic vertex operator algebras at higher central charge
- Time 11/20/2020, Friday, 12:00 (Eastern Time)
- Location Zoom link above
- Abstract Holomorphic vertex operator algebras at central charges up to 24 have been almost fully classified and it appears that they can all be constructed as cyclic orbifolds of lattice vertex operator algebras. At the same time, very little is known about the situation at higher central charge. Intuition from physics tells us that higher central charge analogues of the moonshine vertex operator algebra may exist, but so far all attempts at their construction have failed. The goal of this work is to explore the set of holomorphic vertex operator algebras at higher central charge using non-abelian orbifold theory.
I will begin the talk with a review of the orbifold theory of strongly rational vertex operator algebras. Then I will develop a theory of holomorphic extensions of metacyclic orbifolds as a generalisation of the cyclic theory.
Finally, I will prove the existence of a holomorphic vertex operator algebra at central charge 72 that cannot be constructed as a cyclic orbifold of a lattice vertex operator algebra. If there is time I will discuss some of the challenges arising in trying to construct analogues of the moonshine module.
Some additional talks by members of this seminar
- Speaker Yi-Zhi Huang, Rutgers University
- Speaker Yi-Zhi Huang, Rutgers University
- Title ?????????????????(Representation theory of vertex operator algebras and conformal field theory, in Chinese)
- Event ?????????????????
- Time 11/29/2020, Sunday, 8:30 am Beijing Time or 11/28/2020, Saturday, 7:30 pm Eastern time
- Location See the Tecent meeting link in the web page above
- Abstract ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
- Speaker Yi-Zhi Huang, Rutgers University
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