Descendent invariants for moduli spaces of sheaves

Joint abstract: I will discuss recent work with A. Pixton concerning the relationship between stable maps (Gromov-Witten theory) and sheaves (Donaldson-Thomas theory) for 3-folds. The first talk will be about descendents. For stable maps, descendents involve the cotangent line. For DT
theory, descendents are obtained from the Chern characters of the universal sheaf. The goal of the talk is to explain a descendent correspondence for toric geometries. The second talk will use descendents, relative invariants,
and degeneration to prove correspondences in compact non-toric settings --- including the quintic 3-fold in projective 4 space.