Wall-crossing for Hilbert schemes on CY 4-folds

Invariants counting sheaves on Calabi--Yau 4-folds are obtained by virtual integrals over moduli spaces. These are expressed in terms of virtual fundamental classes, which conjecturally fit into
a wall-crossing framework proposed by Joyce. I will review the construction of vertex algebras in terms of which one can express the WCF.  I describe how to use  them to obtain explicit results for Hilbert schemes of points. As a consequence, I reduce multiple conjectures to a technical proof of the WCF. Surprisingly, one gets a complete correspondence between invariants of Hilbert schemes of CY 4-folds and elliptic surfaces.
 

Link: https://teams.microsoft.com/l/meetup-join/19%3ameeting_ZGRiMTM1ZjQtZWNi…