Integrality of BPS invariants

Ben Davison
(University of Edinburgh )
Seminar
Wednesday, 23 May, 2018, at 16:15-17:15, in Aud. D3 (1531-215)
Abstract:
BPS numbers are certain invariants that "count" coherent sheaves on Calabi-Yau 3-folds. Because of subtleties in the definition, especially in the presence of strictly semistable sheaves, it is not a priori clear that the numbers are in fact integers. I will present a recent proof with Sven Meinhardt of this integrality conjecture. The conjecture follows from a stronger conjecture, namely that a certain constructible function on the coarse moduli space of semistable sheaves defined by Joyce and Song is integer valued. This conjecture in turn is implied by the stronger conjecture that this function is in fact the pointwise Euler characteristic of a perverse sheaf. We prove all of these conjectures by defining this perverse sheaf, and furthermore find that the hypercohomology of this sheaf, which categorifies the theory of BPS invariants, carries a natural Lie algebra structure, generalizing the theory of symmetric Kac-Moody algebras and Yangians.
Organised by: QGM
Contact person: Cristiano Spotti, Martin de Borbon & Roberta Iseppi