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.