Topology Seminar

Date: April 21, 2021

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Siqi He, Simons Center for Geometry and Physics, Stony Brook University

Title: The Hitchin-Simpson equations over Kahler manifold

Abstract: The Hitchin-Simpson equations defined over a K\"ahler manifold are first order, non-linear equations for a pair of a connection on a Hermitian vector bundle and a 1-form with values in the endomorphism bundle. We will describe the behavior of solutions to the Hitchin–Simpson equations with norms of these 1-forms unbounded. We will talk about two applications of this compactness theorem, one is the realization problem of the Taubes' Z2 harmonic 1-form and another is the Hitchin's WKB problem in higher dimensional. We will also discuss the relationship between the analytic compactification and the algebraic compactification.