I am Principal Investigator of the Odysseus research programme ``Geometric and Analytic Properties of Metric Measure Spaces with Spectral Curvature Constraints, with Applications to Manifold Learning'', in short ``GAP_MMS_SCC_AML''. This programme of five years (from 2023 to 2028 ) takes place at the Department of Mathematics and Data Science of the Vrije Universiteit Brussel.

Description :

The Odysseus programme ``GAP_MMS_SCC_AML'' is funded by the Fonds voor Wetenschappelijk Onderzoek (FWO) – Vlaanderen. It is focused on three aspects of geometric analysis.

1. The study of singular spaces obtained as limits of smooth Riemannian manifolds satisfying a uniform spectral constraint on the curvature; such limits appear naturally in geometric evolution problems like Ricci flow or mean curvature flow. 
2. The study of spectral optimization problems on a given smooth manifold; these problems are closely related to the construction of geometrically meaningful representations of the manifold as a subset of a simple ambient space. 
3. The setting up and implementation of new machine learning algorithms for datasets whose underlying geometry satisfies suitable geometric constraints. 

Current team :

Nicolo' Cont, PhD Candidate

Manuel Dias, PhD Candidate

Susovan Pal, Postdoctoral Researcher