Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …

Optimal Transport (OT) has recently emerged as a central tool in data sciences to compare
in a geometrically faithful way point clouds and more generally probability distributions. The …

This open access textbook presents a comprehensive treatment of the arithmetic theory of
quaternion algebras and orders, a subject with applications in diverse areas of mathematics …

" In this chapter, we introduce some of the very basics that are used throughout the book.
First, we give the definition of a topological space and related notions of open and closed …

We discuss equivalent representations of gravity in the framework of metric-affine
geometries pointing out basic concepts from where these theories stem out. In particular, we …

Analysis on metric spaces emerged in the 1990s as an independent research field providing
a unified treatment of first-order analysis in diverse and potentially nonsmooth settings …

This textbook originated from the teaching experience of the first author at the Scuola
Normale Superiore, where a course on optimal transport and its applications has been given …

We develop a geometric framework to study the structure and function of complex networks.
We assume that hyperbolic geometry underlies these networks, and we show that with this …

Encyclopedia of Distances is the result of re-writing and extending our Dictionary of
Distances published in 2006 (and put online http://www. sciencedirect. com/science/book …

We develop a full theory for the new class of Optimal Entropy-Transport problems between
nonnegative and finite Radon measures in general topological spaces. These problems …