Ohio State is in the process of revising websites and program materials to accurately reflect compliance with the law. While this work occurs, language referencing protected class status or other activities prohibited by Ohio Senate Bill 1 may still appear in some places. However, all programs and activities are being administered in compliance with federal and state law.

Algebraic Geometry Seminar - Jun Wang

Algebraic Geometry Seminar
January 14, 2020
3:00 pm - 4:00 pm
Math Tower 154

Title: A mirror theorem for Gromov-Witten theory without convexity

Speaker: Jun Wang - The Ohio State University

Abstract: One central question in Gromov-Witten (GW) theory is to relate the GW invariants of a hypersurface to the GW invariants of the ambient space such as smooth projective variety or orbifold. In genus zero, this is usually done by the so-called quantum hyperplane principle, which uses the twisted GW invariants of the ambient space. This is analogous to the classical theorem that the number of lines inside a cubic surface can be obtained by computing the Euler number of a certain vector bundle on the space of lines inside \mathbb P^3 (which is the Grassmannian G(2,4)). But this approach requires a technical assumption called convexity for the line bundle over the ambient space defining the hypersurface, which can fail for hypersurfaces in orbifolds. In this talk, I will present a way to obtain the genus zero GW invariants of a positive hypersurface in Toric stacks for which the convexity may fail. One key ingredient in the proof is to resolve the genus zero quasimap Wall-Crossing (WC) conjecture proposed by Ionuţ Ciocan-Fontaine and Bumsig Kim, where we don't require the target to be carried with a good torus action as opposed to all previously proven WC examples (or hypersurfaces for which the convexity holds thereof).

Seminar Link

Events Filters: