Joaquin Sanchez Garcia

Short CV

My name is Joaquín Sánchez García, I am currently a math phd candidate at University of Toronto under the supervision of Dr. Robert McCann. I studied Applied Mathematics and Actuarial Science at ITAM and a master in science (math) at Uni-Bonn. I also worked in the mexican mayorist energy market for a while at Cfe calificados in the operations team. I am interested in optimal transport in general, stochastic analysis and applications. Here are some links:

Pre-prints

A pre-print Minimizing movement scheme for aggregation on which we analyze the aggregation equation on compact Riemannian manifolds using the minimizing movement scheme.

Past thesis

My master's thesis (supervised by Dr. Matthias Erbar) can be found as electronic resource (online) or just in this pdf . We study the interplay between curvature conditions in the sense of Bakry-Emery and linear isoperimetry. The study involves understanding functional inequalities in the sense of Markov diffusion semigroups following mostly Analysis and Geometry of Markov Diffusion Operators by Dominique Bakry, Ivan Gentil, Michel Ledoux.

My undergrad thesis (in spanish and supervised by Dr. César Luis García García) is this pdf . We introduce the optimal transport problem, Kantorovich duality and some applications.

Some notes and files

A detailed note Icon on the connections of General relativity and Optimal transport on which we explain the paper of Dr. McCann Displacement convexity of Boltzmann's entropy characterizes the strong energy condition from general relativity.

Another set of notes explaining connections between Ricci curvature bounds and optimal transport, from the graduate analysis seminar. Icon

A short summary of my master thesis (the connection between functional inequalities, curvature bounds and isoperimetry in BE-sense Icon.

Slides (in spanish) of a talk given in 2016 at ITAM on Kakeya sets and the restriction conjecture: Icon.