Joint meeting of the Seminar on Singularities and the ICMS Seminar, with a lecture by Pablo Cuadrado. The program is as follows.
Tuesday, November 18, room 403, IMI-BAS.
13:00 — Giovane Galindo (ICMS, IMI-BAS)
Bundle-type sub-Riemannian structures on holonomy bundles
14:00 — Pablo Portilla Cuadrado (Universidad Politécnica de Madrid)
The medial axis of the Milnor fiber
Abstract (Galindo): In this talk we present the notion of Gromov-Hausdorff distance, a novel field of study that aims to understand the topology of the moduli space of Riemannian metrics on a given manifold. We will then present new results on the subject concerning the collapse of principal bundles onto reductive homogeneous spaces.
Abstract (Cuadrado): Let f(x,y) define an isolated singularity at the origin. In this talk we explore a new flat metric induced on the Milnor fiber of f by the associated complex Hamiltonian vector field. With the help of this metric we can define a spine on each Milnor fiber via the classical method of the medial axis. This spine depends on the choice of boundary for the Milnor fiber. It is subanalytic and comes equipped with a retraction from the boundary onto it. We hope to understand the geometry of the versal unfolding space via these spines. This ongoing joint work with Norbert A’Campo.