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.
DATE: 18 March 2025
SPEAKER: Mauricio Che (University of Vienna)
TITLE: Spaces of Persistence Diagrams and Optimal Partial Transport
ABSTRACT: Persistence diagrams are fundamental tools in Topological Data Analysis, capturing information about the persistent homology of filtrations of data sets. These diagrams can be viewed as measures on the plane and compared using a variant of optimal transport, which we refer to as optimal partial transport. Notably, this approach coincides with a framework introduced by Figalli and Gigli in a different context—a connection first identified by Divol and Lacombe. In this talk, I will examine the geometric properties of spaces of persistence diagrams equipped with optimal partial transport metrics. I will discuss how these properties arise from adaptations of classical results in optimal transport and introduce a generalization of these metrics to objects we call metric pairs. Particular emphasis will be placed on the fact that spaces of measures endowed with the L2-optimal-partial-transport metric exhibit non-negative curvature in the sense of Alexandrov, provided that the background space possesses this property
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DATE: 24 April 2025
SPEAKER: Alice Le Brigant (Sorbonne Université)
TITLE: TBA
ABSTRACT: TBA
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DATE: Thursday 13 February 2025 at 14:00
SPEAKER: Diego Bolón Rodríguez (ULB)
TITLE: A review on highest density region estimation
DATE: Thursday 23 January 2025 at 14:00
SPEAKER: Eddie Aamari (École Normale Supérieure de Paris)
TITLE: A theory of stratification learning: clustering-by-dimensionality with reconstruction
DATE: Thursday 12 December 2024 at 14:00
SPEAKER: Susovan Pal (VUB)
TITLE: Optimal lift, a tool for statistical testing on Singular Shape Spaces
DATE: Wednesday 13 November 2024 at 14:00
SPEAKER: Claire Brécheteau (Nantes Université)
TITLE: Statistical tests for uniformity and iidness on homogeneous spaces
DATE: Wednesday 11 September 2024 at 11:00
SPEAKER: Pierre-Antoine Absil (UCLouvain)
TITLE: Feasible and Infeasible Optimization on Manifolds