Université libre de Bruxelles, 28/06/2018
“Almost Ricci-flat 4-manifolds.”
A manifold is almost Ricci-flat if it admits a sequence of Riemannian metrics with diameter one, for which the Ricci curvature goes to zero uniformly. I will describe results about the topology and geometry of almost Ricci-flat 4-manifolds in the noncollapsed case (joint work with Vitali Kapovitch) and in the collapsed case.
“Bubbling analysis and index estimates for free-boundary minimal hypersurfaces.”
We will discuss some recent results in the analysis of degenerating sequences of free-boundary minimal hypersurfaces (FBMH), with a view to gaining qualitative (and quantitative) relationships between their Morse indices, geometry and topology. A FBMH is a manifold with boundary which is a critical point of the area functional under the sole constraint that its boundary must lie along the boundary of the ambient space. Thus the mean curvature vanishes on the interior and they meet the boundary orthogonally. The Morse index is (roughly speaking) the number of local directions one can push the hypersurface to decrease area. I will present joint works with L. Ambrozio, A. Carlotto and R. Buzano.
“Compactness for Kähler-Einstein manifolds of negative scalar curvature.”
We will discuss compactness for Kahler-Einstein manifolds of negative scalar curvature and geometric Kähler-Einstein metrics on smoothable semi-log canonical models.