The Seminar in Geometry and Statistics takes place monthly at the Department of Mathematics and Data Science of VUB (Building G, Sixth Floor, Room 6.60). It is flexible in terms of schedule and topics, though topics revolve around geometry and statistics. The organizers are Dr. Susovan Pal and myself.
DATE: 19 February 2026
SPEAKER: Fernando Galaz-Garcia (Durham University)
TITLE: Metric geometry of spaces of persistence diagrams
ABSTRACT: Persistence diagrams are central objects in topological data analysis. They are pictorial representations of persistence homology modules and describe topological features of a data set at different scales. In this talk, I will discuss the geometry of spaces of persistence diagrams and connections with the theory of Alexandrov spaces, which are metric generalizations of complete Riemannian manifolds with sectional curvature bounded below. In particular, I will discuss how one can assign to a metric pair (X, A) a one-parameter family of pointed metric spaces of (generalized) persistence diagrams D_p(X, A) with points in (X, A) via a family of functors D_p with p in [1, \infty]. These spaces are equipped with the p-Wasserstein distance when p \geq 1 and the bottleneck distance when p = \infty. The functors D_p preserve natural metric properties of the space X, including non-negative curvature in the triangle comparison sense when p = 2. When p = \infty, the functor D_\infty is continuous with respect to a suitable notion of Gromov–Hausdorff distance of metric pairs. When (X, A) = (R2,\Delta), where \Delta is the diagonal of R2, one recovers previously known properties of the usual spaces of persistence diagrams. I will also discuss some connections of these results with optimal partial transport and Banach space theory.
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DATE: 12 March 2026
SPEAKER: Marco Usula (Oxford University)
TITLE: TBA
ABSTRACT: TBA
DATE: 22 January 2026
SPEAKER: Lynn Delcon (VUB)
TITLE: Boundary Point Detection Methods: An Information-based Comparative Study
DATE: 12 December 2025
SPEAKER: Simon Jacobsson (KU Leuven)
TITLE: A Riemannian geometry of low-rank tensors
DATE: 20 November 2025
SPEAKER: Alexey Lazarev (Toulouse Université)
TITLE: Curvature regularization and Riemannian clustering in the latent space of an autoencoder
DATE: 16 October 2025
SPEAKER: Marie Bormann (Bonn Universität)
TITLE: A gradient flow that is none: Heat flow with Wentzell boundary conditions
DATE: 11 September 2025
SPEAKER: Martin Andersson (Uppsala University)
TITLE: Finite-sample inference for intrinsic dimension via Gaussian kernels
DATE: 24 April 2025
SPEAKER: Alice Le Brigant (Sorbonne Université)
TITLE: The Lp Fisher-Rao metric and the alpha-connection
DATE: 18 March 2025
SPEAKER: Mauricio Che (University of Vienna)
TITLE: Spaces of Persistence Diagrams and Optimal Partial Transport
DATE: 13 February 2025
SPEAKER: Diego Bolón Rodríguez (ULB)
TITLE: A review on highest density region estimation
DATE: 23 January 2025
SPEAKER: Eddie Aamari (École Normale Supérieure de Paris)
TITLE: A theory of stratification learning: clustering-by-dimensionality with reconstruction
DATE: 12 December 2024
SPEAKER: Susovan Pal (VUB)
TITLE: Optimal lift, a tool for statistical testing on Singular Shape Spaces
DATE: 13 November 2024
SPEAKER: Claire Brécheteau (Nantes Université)
TITLE: Statistical tests for uniformity and iidness on homogeneous spaces
DATE: 11 September 2024
SPEAKER: Pierre-Antoine Absil (UCLouvain)
TITLE: Feasible and Infeasible Optimization on Manifolds