Computational optimal transport: mature tools and open problems
Jean Feydy  1@  
1 : Inria Paris-Rocquencourt
Institut National de Recherche en Informatique et en Automatique

Optimal transport is a fundamental tool to deal with discrete and continuous distributions of points.
We can understand it either as a generalization of sorting to spaces of dimension D > 1, or as a nearest neighbor projection under a mass preservation constraint. Over the last decade, a sustained research effort on numerical foundations has led to a x1,000 speed-up for most transport-related computations. This has opened up a wide range of research directions in geometric data analysis, machine learning and computer graphics. 

This talk will discuss the consequences of these game-changing numerical advances from a user's perspective. We will focus on:
1. Mature libraries and software tools that can be used as of 2022, with a clear picture of the current state-of-the-art.
2. New ranges of applications in 3D shape analysis, with a focus on population analysis and point cloud registration.
3. Open problems that remain to be solved by experts in the field.

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