Fwd: Fwd: Geometry and Physics seminars, SISSA

[Math Group]

             When: Thursday 19 January 14:30

             Where: SISSA, room 136

             Speaker: Artan Sheshmani (Harvard University)

             Title: The theory of Nested Hilbert schemes on surfaces

             Abstract: We construct natural virtual fundamental classes for
             nested Hilbert schemes on a nonsingular projective surface S.
             This allows us to define new invariants of S that recover some
             of the known important cases such as  Poincare invariants of
             D\"{urr-Kabanov-Okonek and the stable pair invariants of
             Kool-Thomas. In the case of the nested Hilbert scheme of
             points, we can express these invariants in terms of integrals
             over the products of Hilbert scheme of points on S, and relate
             them to the vertex operator formulas found by
             Carlsson-Okounkov. The virtual fundamental classes of the
             nested Hilbert schemes play a crucial role in the local
             Donaldson-Thomas theory of threefolds that I will talk about,
             in talk 2 (scheduled on Friday 20 14:30 at ICTP).