Seminar

The topological vertex is a powerful formalism first
discovered in physics for computing the Gromov-Witten theory of any
toric Calabi-Yau threefold in terms of a universal power series (the
vertex). Maulik, Nekrasov, Okounkov and Pandharipande found an
equivalent formalism for Donaldson-Thomas invariants in which the
vertex has a very concrete combinatorial interpretation --- it is a
generating function for counting boxes piled in a corner. We present
an orbifold version of the vertex formalism which computes the
Donaldson-Thomas invariants of a toric orbifold. The orbifold vertex
counts boxes which are colored by representations of a finite Abelian
group. As an application, we prove the Donaldson-Thomas Crepant
Resolution Conjecture in the toric case.