Speaker: Jun Li (Stanford University)

Title: Categorification of Donaldson-Thomas invariants

Abstract: : The holomorphic CS functionals of a Calabi-Yau threefold locally realize moduli of stable sheaves as the critical loci of holomorphic functions. We show that the vanishing cycle sheaf of the Chern-Simons functionals can be patched to form a perverse sheaf on the moduli of stable sheaves, and show that the Euler number of the cohomology groups of such sheaves give the Donaldson-Thomas invariants of the Calabi-Yau threefold. We further endow this perverse sheaf with MHM structure, and define the GV numbers of this perverse sheaf. This is a joint work with Young-Hoon Kiem.