Second Meeting of the UK Metric Geometry and Analysis Network

Contribution List

10. Welcome

30/08/2024, 09:00

15. Bi-Lipschitz embeddings of measures with partial transportation distances

Ana Lucía García Pulido (Stirling)

30/08/2024, 09:15

The question of bi-Lipschitz embeddability of Wasserstein spaces into classical Banach spaces has attracted much attention. The importance of such embeddings can be seen, for instance, in the proof of Almgren's partial regularity theorem.

In optimal transport, Wasserstein distances are the prime examples transportation metrics to compare measures of the same total mass. This talk will...

12. Reconstructing the topology of manifolds

Ambrose Yim (Cardiff)

30/08/2024, 10:30

Given finitely many samples on a manifold, can we infer its topological invariants? We discuss some state of the art methods and theoretical bounds for inferring the homology of a manifold from a sufficiently dense point sample. In particular, we describe how these methods are motivated by dynamical systems and Morse theory. Conversely, we also show how these methods can help infer topological...

13. Community Updates

30/08/2024, 11:30

14. Failure of the curvature-dimension condition in sub-Finsler manifolds

Mattia Magnabosco (Oxford)

30/08/2024, 11:45

The Lott–Sturm–Villani curvature-dimension condition CD(K,N) provides a synthetic notion for a metric measure space to have curvature bounded from below by K and dimension bounded from above by N. It has been recently proved that this condition does not hold in any sub-Riemannian manifold equipped with a positive smooth measure, for every choice of the parameters K and N. In this talk, we...

11. Pleijel Nodal domain theorem for the Robin problem on Lipschitz domains

Asma Hassannezhad (Bristol)

30/08/2024, 14:15

The classical Courant nodal domain theorem states that the number of nodal domains of the k-th Dirichlet eigenfunction is bounded above by k. Pleijel later showed that only a finite number of eigenfunctions realised this bound. There have been extensions and improvements of Pleijel's result to the Robin and Neumann boundary conditions requiring boundary regularity that is much stronger than...