Abstract: 

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/ 

Video：http://archive.ymsc.tsinghua.edu.cn/pacm_lecture?html=Kahler_Yang_Mills_equations_and_gravitating_vortices.html