Seminar

Let X be a nonsingular projective 3-fold, one can enumerate pairs (C,D) in which C is an embedded curve in X and D \subset C is a divisor. In this theory one views such pairs as complexes in the derived category of coherent sheaves over X and by constructing the associated moduli space of such pairs and virtual fundamental class one computes the invariants which conjecturally are equivalent to the Gromov-Witten and Donaldson_Thomas invariants after a universal transformation. In this talk I will give a brief review of PT theory and at the end , if time permits, I may explain how one can generalize this theory to higher ranks and what are the obstacles to do so.