Geometry and Physics Seminar: Sheldon Katz

The virtual Poincare polynomials of the stable pair moduli spaces of a Calabi-Yau threefold are conjecturally equivalent to the refined BPS numbers of Gopakumar and Vafa.  As an application, stable pair invariants of the del Pezzo surfaces dP_n determine BPS Hilbert spaces which are observed to be representions of the exceptional Lie algebra E_n, consistent with expectations of string theory.  In another direction, string theory on K3 x T^2 leads to a reduced DT theory on K3, hence
corresponding motivic and refined invariants.  Work in progress on the rational elliptic surface dP_9 ("half K3") suggests that a blend of these two examples leads to a BPS Hilbert space with a representation of affine E_8.  This talk includes separate joint works with Choi, Klemm, and Pandharipande.