Clément Maria
INRIA Sophia Antipolis-Méditerrané and University of Nice
04/11/2021 – h. 1 p.m.
Bio: Clement is a permanent researcher within the DataShape research group at INRIA Sophia Antipolis-Méditerranée, France. My research interests are in Computational Geometry and Topology, with a focus on: Persistent Homology and Low-Dimensional Topology. He is one of the main creators of the C++ software library GUDHI for Topological Data Analysis. He received his PhD in 2014 from the University of Nice and INRIA Sophia Antipolis-Méditerranée, under the supervision of Jean-Daniel Boissonnat. He worked from 2014 to 2017 as postdoctoral fellow within the School of Mathematics and Physics of the University of Queensland, in collaboration with Ben Burton.
Title: Scanning a Riemannian manifold: The intrinsic topological transform.
Abstract: We study the question of whether a space can be recognised uniquely by only capturing elementary topological properties of a collection of linear scans. More specifically, it has recently been proved that
piecewise linear subsets of R^d can be uniquely characterised by their persistent homology when filtered linearly along all directions, the so called persistent homology transform. In this talk, we study the recognition problem for Riemannian manifolds up to isometry, using persistent homology. We introduce Morse functions on the manifold playing the role of ”scans” and inducing a coordinate
system to embed the manifold in a “straighten fashion”. We also study
the stability and approximability of this embedding, and discuss
applications of persistent homology in this framework. This is joint work with Steve Oudot and Elchanan Solomon.
