Seminar

In this work in progress, I consider refined curve counting on local Pezzo surfaces and match to the physically derived formulas of Huang-Klemm-Poretschkin.  Due to the presence of a non-geometric global symmetry in the physics, generating functions for the invariants associated to dP_n (the blowup of n general points in P^2) are supposed to organize as representations of E_n, and as representations of affine E_8 for the rational elliptic surface.  By geometry I define and compute Weyl-invariant characters of a maximal torus associated with the refined BPS invariants.  In all cases to date where the calculation has concluded, these characters coincide with the characters of representations of E_n who dimensions match the predictions of HKP.