at the
American Institute of Mathematics, Pasadena, California
organized by
Nikolas Kuhn, Henry Liu, and Felix Thimm
Specifically, Joyce’s recent "universal" wall-crossing formalism provides a way to systematically study wall-crossing phenomena for a reasonably large class of linear categories. It generalizes previous wall-crossing formalisms of Joyce-Song and Kontsevich-Soibelman, which are controlled by Hall algebras. Strategies that have been successful there may now be applied to new enumerative settings: moduli spaces of sheaves on surfaces, Calabi-Yau 3-folds and 4-folds; for equivariant and/or K-theoretic refinements of ordinary enumerative invariants; etc. Remarkably, the new wall-crossing formula is controlled by a vertex algebra, constructed naturally and geometrically from the moduli stack, indicating new and fruitful interactions with the theory of vertex algebras.
We plan to bring together experts from enumerative geometry, mathematical physics and geometric representation theory to explore connections between these fields through the lens of these new developments.
The main topics for the workshop are:
A report on the workshop activities.