Organizers: Ionut Ciocan-Fontanine, Adeel Khan, Y.P. Lee
Institute of Mathematics, Academia Sinica
We study orbifold Calabi-Yau hypersurfaces in weighted projective stacks from the point of view of the gauged linear sigma model. We give a very brief introduction to the gauged linear sigma model which is a physics version of quasimap theory and review some general conjectures. We explain how these conjectures allow for determination of the orbifold Gromov-Witten invariants without using Gromov-Witten or quasimap theory.
There are two natural ways to deform Joyce's construction of vertex algebras. One is to include tautological insertions, and the other is to work equivariantly. I introduce T-deformed vertex algebras, which unify these two refinements. For the purpose of wall-crossing, they must be treated differently because the associated Lie algebras use different expansions. I will explain this behavior explicitly by studying tautological stable pair wall-crossing and the equivariant 2-loop quiver. Using the calculus of T-deformed vertex algebras developed in an upcoming joint work with E. Bouaziz, we derive 7 new Virasoro algebras for the affine plane.
Archive from Academic Year 2025-26