【讲座】Sub-Riemannian Geometry, Optimal Transport and Isoperimetric Inequalities
2019.03.28 活动

You are cordially invited to the seminar delivered by Samuël Borza from 15:00 – 16:00, March 29th, 2019 (Friday).

 

Topic: Sub-Riemannian Geometry, Optimal Transport and Isoperimetric Inequalities

Time & Date: 15:00 - 16:00 on March 29th, Friday.

Venue: Room 202, Teaching A

Speaker: Samuël Borza, PhD candidate,  Durham University UK.

 

Biography

Samuël Borza completed his Bachelor and Master degree in Mathematical Sciences at the University of Mons in Belgium with a thesis on the Lévy-Gromov inequality in Riemannian geometry. This was done in collaboration with Durham University in the United Kingdom through the European Erasmus+ exchange program. Now pursuing a PhD degree under the supervision of Dr Wilhelm Klingenberg at Durham University, he studies geometric inequalities, such as isoperimetric problems, via optimal transport, in particular in sub-Riemannian manifolds. For this second year of his postgraduate studies, he is staying in Bonn, in Germany, to enjoy the inspiration of the team of the Stochastic and Geometric Analysis Group led by Prof. Dr. Karl-Theodor Sturm at the Hausdorff Institute.

 

Abstract

The legend says that Queen Dido, when founding the great city of Carthage circa 800 BCE, answered the first known isoperimetric question in history : among all the planar shapes with the same perimeter, which one has the largest area? Ever since, this problem and its numerous generalisations have fascinated mathematicians. One of the latest achievements in the field was done with a geodesic foliation of the space, obtained through a Monge transportation of measures. This "needle decomposition" provides a natural proof of the Levy-Gromov isoperimetric inequality in Riemannian manifolds and in metric measure spaces with (synthetic) Ricci curvature bounds. In this talk, I will describe how to adapt this localization technique to sub-Riemannian geometries, providing hope for progress to the challenging isoperimetric problems in Carnot-Caratheodory spaces. I will particularly focus on the Heisenberg groups and the Grushin spaces.

 

All of you are warmly welcomed.

 

School of Science and Engineering

The Chinese University of Hong Kong, Shenzhen