Abstract:

I will define, contextualize and discuss the concept of manifold submetry, which generalizes classical concepts in Riemannian geometry like closed Riemannian foliations and isometric group actions. The particular case of manifold submetries from spheres (spherical manifold submetries) is central to understanding the infinitesimal structure of these objects.

The goal of this talk is to give a panoramic view of recent results connecting algebra, geometry and analysis, which establish a deep connection between spherical manifold submetries and special algebras of polynomials called "Laplacian algebras". This equivalence generalizes Classical Invariant Theory, but has nicer properties that can be exploited to actually obtain new results, even in Invariant Theory itself.

See the full schedule at:

https://www.groups-and-spaces.kit.edu/115_805.php