Lectura de tesis

Título: Symmetries of curved metric measure spaces.

Doctorando: Jaime Santos Rodríguez

Director: Luis Guijarro Santamaría.

Fecha: viernes, 4 de diciembre

Hora: 12:00

Lugar: Sala de grados, Módulo 8, Facultad de Ciencias.

Observaciones: Aforo COVID 21 personas, se debe respetar la distancia

de seguridad y el uso de mascarilla.

Así mismo quienes así lo deseen podrán seguir la presentación mediante

la reunión de Microsoft Teams ” Lectura tesis Jaime Santos Rodríguez

(04/12/2020)”

Resumen: In 2006 Lott, Villani and Sturm defined the notion of

synthetic Ricci curvature bound on a metric measure space. This

definition is formulated in terms of the convexity of an entropy

functional along geodesics in the space of probability measures and is

known as the Curvature-Dimension condition (CD(K,N)). It is known

that in the smooth case this condition is equivalent to having a

lower bound on the Ricci curvature.

Later Gigli, Mondino and Savaré made several refinements, particularly

in the structure of associated Sobolev spaces, in order to avoid

pathological behaviour such as excessive branching of geodesics and

Finsler geometries. Their condition is called Riemannian

Curvature-Dimension condition (RCD(K,N)).

Isometric actions on Riemannian manifolds have been a useful tool to

investigate the interaction between the topology and the Riemannian

metric a manifold might admit.

In this talk I will look at the isometry group of an RCD(K,N) space,

prove that it is a Lie group and, I will discuss what can be done to

ensure that a compact Lie group acts by measure preserving isometries.

LECTURA DE TESIS

Location Fecha: viernes, 4 de diciembre Hora: 12:00