Raphaël Tinarrage

Computing persistent Stiefel-Whitney classes of line bundles, in Journal of Applied and Computational Topology 2021. We define and study characteristic classes within the framework of persistent homology. We implement an algorithm which estimates the orientability of datasets.

Recovering the homology of immersed manifolds, in Discrete & Computational Geometry 2023. 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, Y. Umeda), in Abel Symposium 2018 and 35th International Symposium on Computational Geometry (2019). We define filtrations for persistent homology that are robust to noise and anomalous points.

Empirical analysis of Biding Precedent efficiency in the Brazilian Supreme Court via Similar Case Retrieval (with Henrique Ennes, Lucas E. Resck, Lucas T. Gomes, Jean R. Ponciano, Jorge Poco), preprint, July 2024. We assess the impact of binding precedents on the workload of the Brazilian Supreme Court, through time series of similar cases, and discuss the underlying legal mechanisms.

Train-Free Segmentation in MRI with Cubical Persistent Homology (with Anton François), preprint, January 2024. Segmentation in MRI scans using TDA and without deep learning. Our method is based on the persistent homology of the image and the localization of representative cycles.

LieDetect: Detection of representation orbits of compact Lie groups from point clouds (with Henrique Ennes), preprint, July 2023. An algorithm for the estimation of linear orbits of compact Lie groups from finite samples, allowing to retrieve the precise representation as a sum of irreps.

TDANetVis: Suggesting temporal resolutions for graph visualization using zigzag persistent homology (with Jean Ponciano, Claudio Linhares, Agma Traina, Jorge Poco), preprint, April 2023. An interactive visualization tool for large dynamic graphs, including parameter-suggestion.

Simplicial approximation to CW complexes in practice, preprint, December 2021. We study an algorithm which converts CW complexes into simplicial complexes. We obtain a potential triangulation of the Grassmannian of planes in dimension 4.

O impacto da Súmula Vinculante 26 na diminuição de demanda similar no STF: uma análise quantitativa por modelos de machine learning (with B. Chagas, C. Damian, A. Jaccoud, P. de Oliveira, H. Hennes, J. Poco, J. Ponciano, L. Resck), presented at XI Encontro Internacional do CONPEDI 2022. A comparison of NLP methods for the automatic classification of law documents.

Progressão de regime em crimes hediondos no Supremo Tribunal Federal: uma análise empírica pela Súmula Vinculante 26 (with B. Chagas, C. Damian, A. Jaccoud, P. de Oliveira, H. Hennes, J. Poco, J. Ponciano, L. Resck), presented at XI Encontro Internacional do CONPEDI 2022. An empirical analysis of Brazilian Supreme Court’s Precedent nº 26.

2024, Cálculo Vetorial: Integrais múltiplas, de linha e de superfície, curso de graduação do 2º ano. O objetivo do curso é estudar integrais de funções de várias variáveis, bem como suas aplicações geométricas e físicas. Mais informações na página web do curso.

2023, General and Combinatorial Topology, 3rd year graduation course. Fundamental notions of point set topology (limits, continuity, metrics, compactness, density), and introduction to simplicial topology (including a proof of Borsuk-Ulam theorem). More information on the course page.

2021, Topological Data Analysis with Persistent Homology. 3rd year graduation course. Fundamental notions of point set topology, simplicial homology, persistent homology (with a sketch of proof of the stability theorem). More information on the course page.

PhD dissertation: Topological inference from measures and vector bundles, defended at Laboratoire de Mathématiques d'Orsay, October 2020. Slides and reports.