Using tools coming from topological data analysis (TDA) in order to better understand contact tracing data collected in the Canton of Geneva. This involves modeling interactions among users via simplicial complexes. This is a project done in collaboration with Yann Mentha Loris and supervised by Celia Hacker, Stefania Ebli and Prof. Kathryn Hess. In particular, we develop a user-friendly app allowing to interact with the data in an intuitive and visual manner. Key-concepts : persistent homology, graph time-series, exploratory analysis, graph calibration

Zigzag persistence, as introduced by Carlsson and De Silva, offers a way to better understand the behavior of topological features observed in a family of spaces or pointclouds by generalizing the setting of persistent homology. In this project, we aim at providing a tool to compute levelset zigzag persistence. We deduce the results from computations on extended persistence, which are already implemented in C++. To this end, we make use of Python bindings. This way, we develop an efficient computational tool to add to the general data science toolbox. This project is supervised by Nicolas Berkouk. Key-concepts : zigzag persistence, extended persistence, barcodes, strong diamond principle, relative Mayer-Vietoris diamonds, pyramid theorem, combinatorial bijective mapping

In this project, we aim at making progress in the general setting of applied multi-persistence theory. More precisely, we introduce a distance on extended persistence barcodes of multi-persistence modules and implement an associated efficient automatic differentiation algorithm. This project is supervised by Nicolas Berkouk and Prof. Kathryn Hess. Key-concepts : automatic differentiation algorithm, sheaf theory, barcodes, extended persistent homology, gradient descent

Teaching assistant positions at EPFL, for the following courses. - Analyse I - Physique I pour mathématiciens - Structures Algébriques - Topologie - Algebra The above include individual tutoring, solving problems in front of a class, group tutoring, creation of exercises, grading of homeworks, exercises and midterms, organisational meetings, as well as communication moderating duties (regulating online chat on Zoom).