Optimal Transport and the Calculus of Variations

Scientific Organisers:

David Bourne, Heriot-Watt University
Alpár Mészáros, Durham University
Lucia Scardia, Heriot-Watt University

About:

The aim of this meeting was to bring together experts in the theory of optimal transport and the calculus of variations, with a focus on nonlinear PDEs, gradient flows, and problems with low regularity and singularities. We discussed a range of applications including fluid mechanics, materials science, pattern formation and optimal control.

This workshop was funded by EPSRC Network on Generalised and Low-Regularity Solutions of Nonlinear Partial Differential Equations

Programme:

Monday 11 December
Registration and Refreshments
Welcome and Housekeeping
Guillaume Carlier, Université Paris Dauphine	Displacement smoothness of entropic optimal transport and applications	Abstract
Coffee Break
Thomas Gallouët, Inria Paris	Lagrangian scheme for fluids mechanics based on Semi discrete Optimal Transport	Abstract
Lunch and discussions
Bernhard Schmitzer, Göttingen University	Barycenters for the Hellinger-Kantorovich distance	Abstract
Megan Griffin-Pickering, University College London	The quasi-neutral limit for the ionic Vlasov-Poisson system with rough data	Abstract
Coffee Break
Roger Moser, University of Bath	Analysis of Néel walls in thin ferromagnetic films	Abstract
Tuesday 12 December
Quentin Mérigot, Université Paris-Saclay	Singularities of convex functions and stability of the pushforward by an optimal transport map	Abstract
Coffee Break
Michael Goldman, Université Paris Diderot	From local energy bounds to dimensional estimates in a reduced model for type-I superconductors	Abstract
Eva Kopfer, University of Bonn	Homogenisation of discrete dynamical optimal transport	Abstract
Lunch and discussions
Riccardo Tione, Max Planck Institute, Leipzig	On the Lawson-Osserman conjecture	Abstract
Xavier Lamy, Université Paul Sabatier	On the stability of Möbius transforms of the n-sphere	Abstract
Wednesday 13 December
Lia Bronsard, McMaster University	Patterns in tri-block copolymers: double-bubbles, core-shells and a new partitioning problem	Abstract
Coffee Break
Filippo Santambrogio, Université Claude-Bernard Lyon 1	Strong H^2 convergence of the JKO scheme for the Fokker-Planck equation	Abstract
Alessio Porretta, Università di Roma Tor Vergata	Transport, diffusion and mean field games	Abstract
Lunch
Thursday 14 December
Manuel del Pino, University of Bath	Dynamics of concentrated vorticities in 2d and 3d Euler flows	Abstract
Chloé Jimenez, Université de Bretagne Occidentale	Looking through Wasserstein's glasses and Hilbertian glasses to a muti-agent optimal control problem and the associated Hamilton-Jacobi equation	Abstract
Coffee Break
Jean-Marie Mirebeau, ENS Paris-Saclay	Discretizations of anisotropic PDEs using Voronoi's reduction of quadratic forms	Abstracts
Lunch and discussions
Mateusz Majka, Heriot-Watt University	Polyak-Łojasiewicz inequality on the space of measures and convergence of Fisher-Rao flows	Abstract
Giuseppe Savaré, Bocconi University	Geodesic convexity of entropy functionals in Hellinger-Kantorovich metric	Abstract
Friday 15 December
Yann Brenier, Université Paris-Saclay	Large deviations, Gamma-convergence and large scale computations for the simulation of the early universe	Abstract
Coffee Break
Matthew Thorpe, University of Warwick	Manifold Learning in Wasserstein Space	Abstract
John Ball, Heriot-Watt University	Image comparison and scaling via nonlinear elasticity	Abstract
Lunch