## Geometry and Physics Seminar: Sheldon Katz

- Date: 09/08/2014
- Time: 15:00

University of British Columbia

Refined and motivic BPS invariants

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, hencecorresponding 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.

Location: ESB 4127

Today the seminar has two talks. Sheldon 3-4pm (as usual) and Masoud 4:30-5:30pm. Coffee and cookies are served in between.