A SL_r/PGL_r-correspondence for algebraic surfaces
Prof. Yunfeng Jiang
2024-06-26 9:30-10:30
MCM110
Speaker: Prof. Yunfeng Jiang (University of Kansas)Time: 9:30-10:30 June 26, 2024 (Wednesday)
Venue: MCM110
Title: A SL_r/PGL_r-correspondence for algebraic surfaces
Abstract: For a real 4-dimensional manifold (a smooth projective surface in algebraic geometry) X, the S-duality conjecture implies that we should consider the moduli spaces of stable SL_r-Higgs bundles and stable PGL_r-Higgs bundles on X. The invariants defined by perfect obstruction theories on such moduli spaces are called the Vafa-Witten invariants, which were defined by Tanaka-Thomas in the SL_r side, and by Jiang-Kool in the PGL_r side. In this talk I will talk about the PGL_r/SL_r-correspondence for the Vafa-Witten invariants for these two sides in both K3 surfaces and general type surfaces.
