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.