Prof. Dr. Reto Buzano (Università di Torino)

Abstract
In this talk we will study the space of mean-convex embeddings of spheres and tori into three dimensional manifolds. After motivating the problem, we first start with a non-technical overview of mean curvature flow with surgery and a gluing construction to topologically undo the surgeries again. We then explain how this surgery and gluing approach can be used to prove that the moduli space of mean convex two-spheres embedded in complete, orientable 3-dimensional manifolds with nonnegative Ricci curvature is path-connected. Finally, we study the number of path components of mean convex Heegaard tori, again in ambient 3-manifolds with nonnegative Ricci curvature. We prove that there are always either one or two path components and this number does not only depend on the homotopy type of the ambient manifold. This is joint work with Sylvain Maillot, building on earlier joint work with Robert Haslhofer and Or Hershkovits.

18.06.2026, Zeit: 17:00, Raum: G03-106