Systolic inequalities for minimal projective planes in Riemannian projective spaces

Início: 28/05/2020 17:00

Término: 28/05/2020 18:00

Palestrante: Lucas Ambrozio (University of Warwick)

E-mail do Palestrante:

Resumo: The word "systole" is commonly used in Geometry to denote the infimum of the length of homotopically non-trivial loops in a compact Riemmanian manifold M. In a generalised sense, we may use it also to refer to the infimum of the k-dimensional volume of a class of k-dimensional submanifolds that represent some non-trivial topology of M. In this talk, we will discuss some inequalities comparing the systole to other geometric invariants, e.g. the total volume of M. After reviewing in details the celebrated inequality of Pu regarding the systole of Riemannian projective planes, we will discuss its generalisations to higher dimensions. This is joint work with Rafael Montezuma.