Raphaël Tinarrage

LieDetect: Detection of representation orbits of compact Lie groups from point clouds, with Henrique Ennes. Preprint. An algorithm for the estimation of linear orbits from finite samples, allowing to retrieve the precise representation as a sum of irreps.

Simplicial approximation to CW complexes in practice. Preprint. We study an algorithm which converts CW complexes into simplicial complexes. We obtain a potential triangulation of the Grassmannian of planes in dimension 4.

Computing persistent Stiefel-Whitney classes of line bundles. Published in JACT'21. We define and study characteristic classes within the framework of persistent homology. We define an algorithm which estimates the orientability of datasets.

Recovering the homology of immersed manifolds. Published in DCG'23. We adapt persistent homology to the case of point clouds sampled on a self-intersecting manifold. We deduce a self-intersection-aware clustering algorithm.

DTM-based filtrations, with H. Anai, F. Chazal, M. Glisse, Y. Ike, H. Inakoshi, and Y. Umeda. Published in Abel Symposium'18 and SoCG'19. We define filtrations for persistent homology that are robust to noise and anomalous points.

TDANetVis: Suggesting temporal resolutions for graph visualization using zigzag persistent homology, with Jean Ponciano, Claudio Linhares, Agma Traina and Jorge Poco. Preprint. A parameter-suggestion and interactive visualization tool for large dynamic graphs.

O impacto da Súmula Vinculante 26 na diminuição de demanda similar no STF: uma análise quantitativa por modelos de machine learning. Conference article presented at XI Encontro Internacional do CONPEDI. A comparison of NLP methods for the automatic classification of law documents (in Portuguese).

Progressão de regime em crimes hediondos no Supremo Tribunal Federal: uma análise empírica pela Súmula Vinculante 26. Conference article presented at XI Encontro Internacional do CONPEDI. An empirical analysis of Brazilian Supreme Court’s SV 26 with respect to regime progression (in Portuguese).

Topological inference from measures and vector bundles. PhD dissertation, defended at Laboratoire de Mathématique d'Orsay the 12th of October, 2020. Slides and reports.

2023, General and Combinatorial Topology. 3rd year graduation course. More information on the course page.

2021, Topological Data Analysis with Persistent Homology. 3rd year graduation course. More information on the course page.

I used to conduct the MATh.en.JEANS workshop
in Collège Alain Fournier (Orsay).