Donaldson-Thomas (DT) theory is a modern branch of enumerative and algebraic geometry, taking inspiration from string theory, aiming at counting sheaves on calabi-yau threefolds. I will expose some recent progress on DT theory on crepant resolutions of Calabi-Yau singularities.
I will present a toric localization for DT invariants of toric singularities. I will also speak about a recursive procedure called 'attractor flow tree formula' in order to compute DT invariants in terms of initial data called 'attractor DT invariants'. I will in particular present a joint work with Pierrick Bousseau, Bruno Le Floch and Boris Pioline studying this procedure for the case of the local projective plane, and an ongoing work aiming to describe the attractor DT invariants for all crepant resolutions.