11:00 Sigmundur Gudmundsson (Lund)

Title: Harmonic morphisms from Riemannian homogeneous spaces.
Abstract: Complex-valued harmonic morphisms from Riemannian manifolds, generalize holomorphic functions from Kähler manifolds. Their regular fibres are minimal submanifolds of codimension 2. Harmonic morphisms satisfy both the linear Laplace equation and the non-linear conditions of horizontal (weak) conformality. There exist known examples of homogeneous spaces which allow solutions and others that do not.
Do there exist geometric conditions on $(M,g)$ that ensure existence ?

13:15 Pablo Mira (UP Cartagena)

Title:The classification of constant mean curvature spheres in homogeneous three-spheres.
Abstract: Two highly influential results in the global theory of constant mean curvature surfaces are the Hopf and Abresch-Rosenberg theorems. In the 1950s Hopf proved that any immersed topological sphere of constant mean curvature in a three-dimensional space form is a round sphere. In 2004 Abresch and Rosenberg proved that any immersed topological sphere of constant mean curvature in a rotationally symmetric homogeneous three-manifold is a sphere of revolution. In this talk I will explain the Hopf and Abresch-Rosenberg theorems, together with a recent theorem obtained in collaboration with W.H. Meeks, J. Pérez and A. Ros: the classification of immersed constant mean curvature spheres in an arbitrary simply connected, compact homogeneous three-manifold.

14:30 Josef Dorfmeister (TU Munich)

Title: Minimal surfaces in $Nil_3$ via loop groups.
Abstract: We will discuss surfaces in $Nil_3$ in the spirit of the work of Taimanov and Berdinskii. Starting from Berdinskii's system of equations for conformal immersions into $Nil_3$ we chracaterize constant mean curvature surfaces by flat connections and equivalently by the harmonicity of some map. In this context we clarify what it means for an arbitrary conformal surface to have a holomorphic Abresch-Rosenberg differential. It turns out that the Berdinskii system produces "associate families" of surfaces, but, in general, only for a few values of the family parameter the corresponding surface can have constant mean curvature. If the mean curvature H vanishes, however, a complete loop group method is available. In particular, every minimal surface in $Nil_3$ can be constructed starting from some holomorphic (and unconstrained) data.

16:00 Steen Markvorsen (DTU)

Title: A geometric angle on heat kernels, parabolic waves, and wildfires.
Abstract: Negative sectional curvatures tend to distribute heat kernels relatively fast in comparison with the flat case. This suggests that the speed of travelling parabolic waves should be correspondingly larger on a negatively curved background. We give simple examples of this phenomenon and indicate applications to the current understanding of the spread of wildfires in general Riemannian manifolds.