Raphaël Tinarrage

raphael.tinarrage[at]fgv.br

FGV EMAp, Praia de Botafogo, nº190
5º Andar - Sala 514
Rio de Janeiro, Brasil


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



Research

On the theoretical side, my research interests include persistent homology, varifolds theory and combinatorics of simplicial complexes.

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.

I also work on concrete applications of Topological Data Analysis and machine learning.

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).

My PhD thesis can be found here:

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


Code

My work is implemented in the package velour for Python. It can be downloaded via PyPI or GitHub.


Teaching

At FGV EMAp, I gave two summer courses:

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.

At Université Paris-Sud, I was assistant professor for the following courses:

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.

Talks and posters

5 Oct 2023 Online, Dynamical Systems & Applications, TDA 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 pra escolha de resolução temporal na visualização de grafos
14 Sept 2022 Santiago, XI Encontro do CONPEDI, O impacto da SV 26 na diminuição de demanda similar no STF
13 Sept 2022 Santiago, 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

Misc.

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