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.

Brian Weber (University of Pennsylvania, USA) will speak in the geometry seminar on Tuesday 9 May, at 2pm in the Salle de Profs. Brian’s title is Potential theory and first order equations on degenerating 4-manifolds.

Felix Schlenk (Université de Neuchâtel, Switzerland) will speak in the geometry seminar on Tuesday 11 June, at 11.30am in the Salle de Profs. Felix’s title and abstract are to be announced.

Matthias’s title is Manning’s inequality for Finsler and Reeb flows and his abstract is below.

I will explain parts of recent work with Marcelo Alves and Alberto Abbondandolo, in which we study entropy rigidity for Reeb flows and Finsler flows. An important result in the study of the topological entropy for geodesic flows is Manning’s inequality, that bounds the topological entropy from below by the volume entropy.
I will discuss two ways to extend this result to Finsler and Reeb flows.

Claude LeBrun (Stony Brook University) will speak in the geometry seminar on Wednesday 26 of June. Claude’s title is Einstein Metrics, Harmonic Forms, and Conformally Kähler Geometry and his abstract is below.

There are certain compact 4-manifolds, such as real and complex hyperbolic 4-manifolds, 4-tori, and K3, where we completely understand the moduli space of Einstein metrics. But there are vast numbers of other 4-manifolds where we know that Einstein metrics exist, but cannot currently determine whether or not there are other Einstein metrics on them that are qualitatively different from the currently-known ones. In this lecture, I will first present a characterization of the known Einstein metrics on Del Pezzo surfaces that I discovered several years ago, and then describe a delicate generalization which I obtained only quite recently.