January 11, 2023
TITLE: Wall-crossing for Calabi-Yau fourfolds and applications
ABSTRACT: To count SU(4)-instantons on Calabi-Yau fourfolds, Borisov-Joyce and later on Oh-Thomas formulated a theory which counts Gieseker stable sheaves. An interesting question is what happens when one changes the stability condition and crosses walls where sheaves get destabilized. Relying on the ideas introduced by D. Joyce, I will explain a formulation of wall-crossing that is particularly useful in solving existing conjectures by discussing some of its applications.