Categorification of Donaldson-Thomas Invariants

Explore a lecture on the categorification of Donaldson-Thomas invariants presented by Marco Robalo from Sorbonne Universite at the M-Seminar, Kansas State University. Delve into the construction of a perverse sheaf over a (-1)-shifted derived scheme X with suitable orientation data, as developed by Brav-Bussi-Dupont-Joyce-Szendroi (BBDJS). Examine how this construction utilizes a Darboux local form for (-1)-shifted symplectic schemes and recovers Behrend's counting of Donaldson-Thomas invariants through Euler characteristics. Discover an ongoing collaborative work with B. Hennion and J. Holstein, which proposes a strategy based on Toën-Vezzosi derived foliations to glue a sheaf of 2-periodic dg-categories over X, locally modeled on matrix factorization categories MF(U,f). Learn how this approach aims to recover and extend the BBDJS construction, offering new insights into the categorification of Donaldson-Thomas invariants.

Marco Robalo - Categorification of Donaldson-Thomas invariants