I will present Topological Data Analysis, in particular persistent homology theory. This theory, which has widely invested the fields of computational geometry and data analysis since the 2000's, allows to apply theoretical tools from algebraic topology (in particular, the singular homology of topological spaces). On the theoretical side, persistent homology offers an answer to the following estimation problem: given a submanifold M of a Euclidean space, and a finite point cloud X that we suppose close to the submanifold, estimate the singular homology groups of M from the simple observation of X. On the application side, it can be used as an exploratory tool to discover the topology of datasets, or as a new feature in machine learning tasks. In this talk I will define persistent homology, and show how one interprets the persistence barcodes.
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I did the essential part of my mathematical education at the Institut de Mathématiques d'Orsay, in the south of Paris. I passed by the ENS Saclay, where I obtained my agrégation (teaching diploma). I then followed a research master in mathematics applied to life sciences. I did a Ph.D. in Topological Data Analysis, under the supervision of Frédéric Chazal and Marc Glisse, in the DataShape team (INRIA Saclay). I developed variations of persistent homology theory in order to solve topological inference problems. I am now a post-doc at EMAp, pursuing my missions to develop and apply Topological Data Analysis. Apart from doing math, I like teaching math (especially confronting young students with research), understanding the topology of the world around me, and doing capoeira.