Title: Tits buildings and their reflections on geometry
Abstract: Tits building is a fundamental tool invented by Tits for the studies of algebraic groups, which was applied historically to give the first proof of the celebrated Mostow rigidity. In this talk I will give a very brief survey on Tits building and a few of its reflections on differential geometry.
Title: A Universal Property for Differentiable Manifolds
Abstract: The talk will offer a very simple general strategy for how to verify some important statements for various classes of manifolds. This will encompass three results about de Rham cohomology: de Rham’s isomorphism theorem, Poincaré duality, and the Künneth-Leray-Hirch theorem for fiber bundles. It will also include the general version of Whitney’s embedding theorem.
Title: Manifold submetries and polynomial algebras.
Abstract: Manifold submetries generalize Riemannian submersions, isometric group actions, and isoparametric maps. The local structure of Riemannian submersions around a point, is determined by Riemannian submersions from round spheres. In this talk, we will prove a surprising equivalence between the class of Riemannian submersions from spheres, and a class of polynomial algebras, with applications, for example, to Invariant Theory. This is based on a joint work with Ricardo Mendes.
Title: Odd-dimensional nonnegatively curved GKM-manifolds
Abstract: We prove that for odd-dimensional, closed, connected, orientable, non-negatively curved GKM_3 manifolds both the equivariant and the ordinary real cohomology split off the cohomology of an odd-dimensional sphere. This is joint work with Christine Escher and Oliver Goertsches.