Wasserstein Jam

The aim of this online meeting is to gather young researchers working on different aspects of the Wasserstein space. The format is thought to take advantage of being remote while trying to mitigate the cons: there will be (many) more talks than in a traditional in-person meeting, each one quite short (20 minutes) with the possibility to be light on the basics since the audience is expected to be relatively fluent with $\mathscr{P}_2$. The speakers are also welcome to drift away from a classical presentation to dwell on results that they like and wish to propagate, specific difficulties or known problems that are not so obvious to the non-expert, future directions of interest...

Jam information

Date: October 27, 2026
Meeting link: using the open-source Jitsi. No account nor app needed, you connect from a browser.
https://meet.jit.si/moderated/f81ef81ea18228e1b0e8f9dc1566db7b6839041c2a5b7495e668db3425048f52

Tentative program (here PDF version)

	Speaker	Title	Abstract
8h30 - 8h50	Théo Lavier Université de Toulon	Application of Semi-Discrete OT for Atmospheric Dynamics	The Semi-Geostrophic (SG) equations provide a powerful model for large-scale atmospheric dynamics. Through a coordinate transformation, the SG system can be recast as an OT problem. In this talk, we present a semi-discrete OT framework that discretizes the target measure into Lagrangian particles, reducing the PDE to a finite-dimensional system of ODEs driven by the centroids of Laguerre cells. We discuss existence, regularity, and energy conservation of these discrete solutions for both incompressible and compressible flows. Finally, we highlight recent progress on the physical pullback problem: reconstructing divergence-free, volume-preserving physical velocity fields from discrete centroid trajectories via finite-element stream functions.
8h50 - 9h10	Alessandro Tedeschi Scuola Normale Superiore	TBA	TBA
9h10 - 9h30	Fernanda Urrea INSA Rouen Normandie	TBA	TBA
Break
10h00 - 10h20	Filip Voronine University of Delft	TBA	TBA
10h20 - 10h40	Ivan Romanò Università di Trento	TBA	TBA
10h40 - 11h00	Alessandro Cosenza Institut de Mathématique d'Orsay	An introduction to branched optimal transport	Branched optimal transport is a variant of optimal transport in which an economy of scale principle is present. Grouped transportation is favoured, leading to mass moving on branching networks. In this talk we provide a short introduction to the topic, starting from Gilbert's classical model for finite networks and then passing to the continuous models by Xia and by Bernot, Caselles and Morel. Moreover, we present some open question on the "fractal" behaviour of branched transportation.
Break
11h30 - 11h50	Federico Renzi Scuola Normale Superiore	TBA	TBA
11h50 - 12h10	Ernesto Treumún ENSTA Paris Saclay	Clarke subdifferential on Wasserstein spaces (and applications to optimal control)	The study of the differential structure of the Wasserstein space $\mathscr{P}_2(\mathbb{R}^d)$ is well known, and it is a key ingredient in obtaining optimality conditions for a broad class of problems, such as mean-field games, mean-field limits, and optimal control problems. However, the class of smooth functions on $\mathscr{P}_2(\mathbb{R}^d)$ is rather limited; even the squared Wasserstein distance fails to be smooth unless restrictive assumptions are imposed on the measures. In this talk, I will present a joint work with Fernanda Urrea in which we introduce a non-smooth object that allows us to tackle this issue: the Clarke subdifferential on the Wasserstein space. We will study this subdifferential, its main properties and see explicit examples for different functionals on $\mathscr{P}_2(\mathbb{R}^d)$. At the end of the talk, I will show some applications to optimal control on $\mathscr{P}_2(\mathbb{R}^d)$.
12h10 - 12h30	Arthur Schichl ETH Zurich	TBA	TBA
Lunch break
15h00 - 15h20	Alessandro Pinzi Bocconi	The Wasserstein geometry of random measures through superposition principles	In this talk, I will introduce the space of random measures $\mathcal{P}_p(\mathcal{P}_p(X))$, endowed with the Wasserstein-on-Wasserstein metric, where $(X, d)$ is a complete separable metric space. In this setting, we prove a metric superposition principle that will allow us to recover important geometric features of the space. When $X$ is $\mathbb{R}^d$, we will see also the differential structure of $\mathcal{P}_p(\mathcal{P}_p(\mathbb{R}^d))$ in analogy with the classic Wasserstein space $\mathcal{P}_p(\mathbb{R}^d)$. We show that continuity equations for laws of random measures involving the abstract concept of derivation acting on cylinder functions can be more conveniently described by suitable non-local vector fields $b:[0,T] \times \mathbb{R}^d \times \mathcal{P}_p(\mathbb{R}^d) \to \mathbb{R}^d$. In this way, we can: characterize the absolutely continuous curves on the Wasserstein-on-Wasserstein space; define and characterize its tangent bundle; prove a Benamou-Brenier-like formula; prove a superposition principle for the solutions to the standard non-local continuity equation in terms of solutions of interacting particle systems. The talk is based on a joint work with Giuseppe Savaré.
15h20 - 15h40	Kexin Lin Institut Camille Jordan	TBA	TBA
15h40 - 16h00	Fanch Coudreuse Institut Camille Jordan	TBA	TBA
Break
16h30 - 16h50	David Lenze Karlsruhe Intitute of Technology	On tangent cones and rigidity of Wasserstein spaces	In this talk I will introduce and motivate the notion of inner tangent cones, discuss their relationship to the classical tangent cones, and explain the role they play in my recent work on the rigidity of Wasserstein spaces.
16h50 - 17h10	Christophe Vauthier Institut de Mathématique d'Orsay	TBA	TBA
17h10 - 17h30	Nicolas Lanzetti Caltech	From $\mathbb{R}^d$ to $\mathscr{P}(\mathbb{R}^d)$ and back: the variational structure of the Wasserstein space	Working in the space of probability measures permits us to escape brittle finite-dimensional parametrizations of probability measures, and is therefore natural in a variety of applications such as machine learning and distributionally robust optimization. However, the space of probability measures is not a vector space and, thus, many classical methods available in the optimization literature (e.g., derivatives) are of little help. Thus, one typically has to resort to the abstract machinery of infinite-dimensional analysis or other ad-hoc methodologies, which are, however, not tailored to the space of probability measures, generally entail projections or require convexity-type assumptions, and break when the problem changes. In this talk, I will discuss how we can endow the Wasserstein space (i.e., the space of probability measures equipped with the Wasserstein distance) with a variational structure which enables the study of optimality conditions that (i) resemble rationales of Euclidean spaces, such as KKT conditions, and (ii) are intuitive, informative, and easy to study. Then, I will show how the optimality conditions can be applied in practical applications such as learning diffusion processes and training generative models.