Wall-crossing for Calabi-Yau fourfolds and applications

Abstract: My work focuses on proving wall-crossing for sheaves and pairs on Calabi-Yau fourfolds. It is desirable that the end result can have many concrete applications to existing conjectures. For this purpose, I introduce a new structure into the picture - formal families of vertex algebras. Apart from being a natural extension of the vertex algebras introduced by Joyce, they allow to wall-cross with insertions instead of the plain virtual fundamental classes. Many fundamental hurdles needed to be overcome to prove wall-crossing in this setting. They included constructing Calabi-Yau four obstruction theories on (enhanced) master spaces and showing that the invariants counting semistable torsion-free sheaves are well-defined. At the end, I will use the complete package to address existing conjectures with applications to 3-fold DT/PT correspondences.

algebraic geometryrepresentation theory

Audience: researchers in the topic

Algebra and Geometry Seminar @ HKUST

Series comments: Algebra and Geometry seminar at the Hong Kong University of Science and Technology (HKUST).

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