PROFESOR: Natalia Jonard (Universidad Autónoma de México)

TÍTULO: “Group actions on hyperspaces of convex sets and Banach-Mazur compacta”

FECHA Y HORA: 7 de Noviembre a las 12:00h.

LUGAR: Seminario del IUMPA (Universitat Politècnica de València).

ABSTRACT: For every n 2 N, the Banach Mazur compactum BM(n) is defined as the set of isometry classes of n-dimensional Banach spaces topologized by the following metric best known in Functional Analysis as the Banach-Mazur distance: d(E,F)=ln inf {||T||•||T-¹|| T : E → F is a linear isomorphism } The original geometric representation of BM(n) is based on the one-to-one correspondence between norms and odd symmetric convex bodies. This representation establishes a natural link between the Banach-Mazur compacta and some quotient spaces of hyperspaces of convex sets.

In this talk, we will use the natural action of certain groups of afine transformations with the following two main objectives: 1) to understand the topological structure of certain Hyperspaces of convex sets and 2) to find new topological models for the Banach-Mazur Compacta.