Raphaël Tinarrage

LieDetect: Detection of representation orbits of compact Lie groups from point clouds (with Henrique Ennes), to appear in Foundations of Computational Mathematics 2025. An algorithm for estimating linear orbits of Lie groups from finite samples, that also recovers the exact representation as a sum of irreps.

Empirical analysis of binding precedent efficiency in Brazilian Supreme Court via case classification (with Henrique Ennes, Lucas Resck, Lucas T. Gomes, Jean R. Ponciano, Jorge Poco), in Artificial Intelligence and Law 2025. We assess the impact of binding precedents at the Brazilian Supreme Court level, through time series of similar cases, and discuss the underlying legal mechanisms.

ZigzagNetVis: Suggesting temporal resolutions for graph visualization using zigzag persistence (with Jean Ponciano, Claudio Linhares, Agma Traina, Jorge Poco), in IEEE Transactions on Visualization and Computer Graphics 2025. Interactive visualization tool for large dynamic graphs with parameter-suggestion.

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 Hirokazu Anai, Frédéric Chazal, Marc Glisse, Yuichi Ike, Hiroya Inakoshi, Yuhei Umeda), in Abel Symposium 2018 and International Symposium on Computational Geometry 2019. We define filtrations for persistent homology that are robust to noise and anomalous points.

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.

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.

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

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.