Wall-crossing for Calabi-Yau 4-folds

This is meant to be an informal crash course on some recent wall-crossing conjectures in Enumerative Geometry. The goal is to understand a concrete application of wall-crossing to the computation of some Donaldson-Thomas type invariants for Calabi-Yau 4-folds.

References:

• A. Bojko, Wall-crossing for zero-dimensional sheaves and Hilbert scheme of points on Calabi-Yau 4-folds, arXiv, 2021.

• J. Gross, D. Joyce, Y. Tanaka, Universal structures in ℂ-linear enumerative invariants theories. I, arXiv, 2020.

Schedule:

• Background on Vertex Algebras, Dirk van Bree (Utrecht), 6 May 2021, 13.00-15.00 (CEST timezone), notes.

• Stability conditions and wall-crossing, Sergej Monavari - Martijn Kool (Utrecht), 11 May 2021, 13.00-15.00 (CEST timezone), notes and notes.

• Wall-crossing of topological pairs, Andrea Ricolfi - Solomiya Mizyuk (SISSA) 19 May 2021, 10.00-12.00 (CEST timezone), notes and notes.

• Cao-Kool conjecture for Calabi-Yau 4-folds, Younghan Bae - Woonam Lim (ETH) 28 May 2021, 10.00-12.00 (CEST timezone), notes and notes.