| Speaker: | Shengjing Xu (UPenn) (University of Pennsylvania) |
|---|---|
| Title: | Holomorphic Lagrangians in Higgs and de Rham Moduli Spaces |
| Date (JST): | Thu, Jun 25, 2026, 13:30 - 15:00 |
| Place: | Seminar Room B |
| Abstract: |
The moduli spaces of Higgs bundles and flat connections on a Riemann surface are fundamental examples of holomorphic symplectic manifolds, lying at the intersection of integrable systems, geometric representation theory, and quantum field theory. In this talk, I will describe holomorphic Lagrangian subvarieties in the moduli spaces of Higgs bundles and flat connections, constructed by specifying a sub-line bundle inside a rank-n vector bundle. These Lagrangians are naturally labeled by divisors: on the Higgs side, they are related to Baker–Akhiezer divisors, while on the de Rham side they correspond to apparent singularities of flat connections. I will further explain how these constructions lead to Lagrangian correspondences between the Higgs (respectively, de Rham) moduli spaces and Hilbert schemes of points on the (respectively, twisted) cotangent bundle of the Riemann surface. Connections to the geometric Langlands program will be briefly discussed. |
