Raphaël Tinarrageraphael.tinarrage[at]fgv.br Escola de Matemática Aplicada (FGV EMAp)

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.
TrainFree 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 parametersuggestion. 


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. 


Computing persistent StiefelWhitney 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 selfintersecting manifold. We deduce a selfintersectionaware clustering algorithm. 


DTMbased 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. 


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:
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. 

Code
My PhD work is implemented in the packagevelour
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).
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.
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 BorsukUlam 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. 

Assistant professor at Université ParisSaclay.
20172019  M257  TD Equations différentielles ordinaires, L2 BiologieChimie. More information here. 
20172020  M331  TP Inférence statistique, L3 MINT. 
20172020  M326  TD Projet modélisation et calcul scientifique, L3 MINT. 
Students
During my postdoc at FGV EMAp, I advised two student's projects.
20212023  MSc student Henrique Hennes, Adaptation of tools from Lie geometry to Data Analysis 
20212023  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 CWcomplexes in practice  
8 June 2021  Online, SoCG Minisymposium Comp. Top., Simplicial approximation to CWcomplexes 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 StiefelWhitney classes  
Dec 2020  UMPA Lyon, Séminaire EDP Modélisation, Inférence topologique avec l'homologie persistante  
Nov 2020  Online, EPFL Applied Topology Seminar, Persistent StiefelWhitney classes  
Oct 2020  Orsay LMO Univ. ParisSud, 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 StiefelWhitney  
Oct 2019  Inria Saclay, Datashape seminar, Recovering the homology of immersed manifolds  
June 2019  Portland, Symposium on Computational Geometry, DTMbased filtrations  
June 2018  IST Austria, Algebraic Topology: Methods, Computation and Science, DTMbased filtrations 