Raphaël Tinarrage

raphael.tinarrage[at]fgv.br

Escola de Matemática Aplicada (FGV EMAp)
Praia de Botafogo, nº190, 5º Andar, Sala 514
Botafogo, Rio de Janeiro, Brasil

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link to github link to youtube link to arxiv link to google scholar link to HAL link to orcid link to theses.fr

Postdoc at FGV EMAp, advised by César Camacho.
Former PhD Student at Laboratoire de Mathématiques d'Orsay and Inria Datashape, advised by Frédéric Chazal and Marc Glisse.
Here is my curriculum vitae and a list of publications.

Research

My work revolves around Topological Data Analysis (TDA), in its theoretical developments and practical applications.

Topological inference with TDA: Stability and consistency of Persistent Homology, estimation of topological invariants other than homology groups, varifold formalism, and detection of Lie group symmetries. I am interested in obtaining stability bounds that involve the Wasserstein distance, more suited to deal with datasets containing noise or anomalous points.

Combinatorial topology: Triangulation of topological spaces, simplicial approximation, and Lusternik–Schnirelmann category. In practice, computational topology suffers from the fact that homotopical invariants quickly become intractable (e.g., the contractibility of simplicial complexes of dimension 4 or more is undecidable), hence alternatives must be found, employing heuristics or additional topological knowledge.

Concrete applications: Medical Image Analysis, Visualization of large graphs, Natural Language Processing (with a focus on Brazilian law), Statistics on Phylogenetic Trees Spaces, and Equivariant Neural Networks.

link to arxiv

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.

link to arxiv

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.

link to arxiv

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.

link to arxiv

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.

link to arxiv

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.

link to arxiv

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.

link to arxiv

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.

link to arxiv

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


Conference articles written in Portuguese:

link to arxiv

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.

link to arxiv

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.

Code

My PhD work is implemented in the package velour for Python. It can be downloaded via PyPI or GitHub.
My others articles are also implemented in Python and available on my GitHub page.

Teaching

Graduation course at FGV EMAp (in portuguese).

link to course page

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.

Summer courses at FGV EMAp.

link to course page

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.

link to 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.

Assistant professor at Université Paris-Saclay.

2017-2019 M257 TD Equations différentielles ordinaires, L2 Biologie-Chimie. More information here.
2017-2020 M331 TP Inférence statistique, L3 MINT.
2017-2020 M326 TD Projet modélisation et calcul scientifique, L3 MINT.

Students

During my post-doc at FGV EMAp, I advised two student's projects.

2021-2023 MSc student Henrique Hennes, Adaptation of tools from Lie geometry to Data Analysis
2021-2023 Undergraduate students Beatriz S. Chagas, Ana C. M. Jaccoud, Carla M. Damian and Pedro B. de Oliveira,
Development of Data Analysis techniques for Brazilian legal documents.

Talks and posters

8 Mar 2024 FGV Rio, Brazilian Workshop on Continuous Optimization, LieDetect
31 Jan 2024 Online, Datashape Seminar, LieDetect
5 Oct 2023 Online, Dynamical Systems & Applications, Minicourse IV: Python tutorial
3 Oct 2023 Online, Dynamical Systems & Applications, TDA Minicourse III: Persistent homology
28 Sept 2023 Online, Dynamical Systems & Applications, TDA Minicourse II: Homological inference
26 Sept 2023 Online, Dynamical Systems & Applications, TDA Minicourse I: Topological invariants
26 Jan 2023 FGV Rio, Summer School on Data Science, TDA Minicourse III: Persistent homology
26 Jan 2023 FGV Rio, Summer School on Data Science, TDA Minicourse II: Homological inference
25 Jan 2023 FGV Rio, Summer School on Data Science, TDA Minicourse I: From topology to data analysis
19 Jan 2023 FGV Rio, Workshop On Legal Digital Intelligence, TDA and Súmulas Vinculantes
24 Nov 2022 USP São Carlos, ICMC Seminário, Análise Topológica de Dados e suas aplicações
21 Nov 2022 USP São Carlos, ICMC Seminário, TDA para escolha de resolução temporal na visualização de grafos
14 Sept 2022 Santiago, Chile, XI Encontro do CONPEDI, O impacto da SV 26 na diminuição de demanda similar no STF
13 Sept 2022 Santiago, Chile, XI Encontro do CONPEDI, Progressão de regime em crimes hediondos no STF
June 2022 Mathematical Institute Oxford, ATMCS, Simplicial approximation to CW-complexes in practice
8 June 2021 Online, SoCG Minisymposium Comp. Top., Simplicial approximation to CW-complexes in practice
9 June 2021 Online, EMINES, Analyse Topologique des Données II : Homologie persistante
26 May 2021 Online, EMINES, Analyse Topologique des Données I : Invariants topologiques
April 2021 FGV Rio, EMAp Seminário, Topological inference in TDA II: Persistence barcodes
April 2021 FGV Rio, EMAp Seminário, Topological inference in TDA I: Topology in datasets
Dec 2020 Applied Algebraic Topology Network, Persistent Stiefel-Whitney classes
Dec 2020 UMPA Lyon, Séminaire EDP Modélisation, Inférence topologique avec l'homologie persistante
Nov 2020 Online, EPFL Applied Topology Seminar, Persistent Stiefel-Whitney classes
Oct 2020 Orsay LMO Univ. Paris-Sud, PhD Defense, Topological inference from measures and vector bundles
June 2020 Online, Symposium of Computational Geometry, Recovering the homology of immersed manifolds
May 2020 LMO Orsay, Séminaire informel, Introduction à l'homologie persistante
Mar 2020 Inria Saclay, Datashape seminar, Introduction aux classes de Stiefel-Whitney
Oct 2019 Inria Saclay, Datashape seminar, Recovering the homology of immersed manifolds
June 2019 Portland, Symposium on Computational Geometry, DTM-based filtrations
June 2018 IST Austria, Algebraic Topology: Methods, Computation and Science, DTM-based filtrations

Miscellaneous

link to page I used to conduct the MATh.en.JEANS workshop in Collège Alain Fournier (Orsay). It is an introduction to research for middle school students, resulting in a scientific-like article.
link to pdf document A gentle introduction to persistent homology, in French.