Archives for August 2019

Ruadhai Dervan (University of Cambridge) will speak in the geometry seminar on Tuesday 3 December 2019 at 11am in the Salle de Profs. (Ruadhai’s talk was initially planned for the 29th of October but has been moved). Ruadhai’s title is Optimal symplectic connections on holomorphic submersions and his abstract is below:

One can think of a Hermite-Einstein metric on a holomorphic vector bundle over a Kähler manifold as determining a canonical choice of Fubini-Study metric on each fibre of the projectivisation of the bundle. I will describe an equation which makes sense for much more general fibrations and (conjecturally) determines a canonical choice of fibrewise constant scalar curvature Kähler metric on each fibre. The main result will use these new metrics to give a novel construction of constant scalar curvature Kähler metrics on the total space of such fibrations. Time permitting, I will describe a largely conjectural picture which explains the geometric significance of these equations. This is joint work with Lars Sektnan.

Juan Criado del Rey (KU Leuven) will speak in the geometry seminar on Tuesday 24 September 2019 at 11am in the Salle de Profs. Juan’s title is Minimal energy configurations on compact manifolds and his abstract is below.

Distributing points on spheres and other manifolds is a very classical problem. Its modern formulation in terms of energy-minimizing configurations is due to the discoverer of the electron J. J. Thomson who in 1904 posed the question: “In which position (within some set such as a ball or a sphere) would N electrons lie in order to minimize their electrostatic potential?” In this talk I will present some results about minimal energy points on compact manifolds and I will introduce a couple of connections to problems in Numerical Analysis.