Kähler-Yang-Mills equations and gravitating vortices

Speaker:Oscar Garcia-Prada (Consejo Superior de Investigaciones Científicas)
Schedule:Fri., 16:00-17:00, May 17, 2024
Venue:Lecture Hall C548, Tsinghua University Shuangqing Complex Building A(清华大学双清综合楼A座C548报告厅); Zoom Meeting ID: 271 534 5558 Passcode: YMSC


The search for canonical metrics on manifolds and vector bundles is one of the most natural problems in geometry. In this talk, I will intruduce a system of coupled differential equations, known as  the Kähler-Yang-Mills equations on a holomorphic vector bundle over a compact complex manifold. These equations, inspired by the Donaldson--Uhlenbeck--Yau theorem  for bundles and the Yau–Tian–Donaldson conjecture for constant scalar curvature Kähler metrics, intertwine the curvature of a Hermitian–Yang–Mills connection on the bundle  and the scalar curvature of a Kähler metric on the manifold. After this, I will consider special symmetric solutions on a compact Riemann surface known as gravitating vortices.

Speaker's website: https://www.icmat.es/miembros/garcia-prada/