Workshop

Optimal Transport and the Calculus of Variations

11 - 15 Dec 2023

ICMS, Bayes Centre, Edinburgh

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Organiser

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

Meet the speakers

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

Abstract

Thomas Gallouët

Inria Paris

Lagrangian scheme for fluids mechanics based on Semi discrete Optimal Transport

Abstract

Lunch and discussions

Abstract

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

Abstract

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

Abstract

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

Abstract

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

Abstract

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

Abstract

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

Abstract

Jean-Marie Mirebeau

ENS Paris-Saclay

Discretizations of anisotropic PDEs using Voronoi's reduction of quadratic forms

Abstracts

Lunch and discussions

Abstracts

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

Abstract

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

Abstract