Steve Oudot

Directeur de Recherche, Inria
Professeur Chargé de Cours, École Polytechnique

Address:


 Inria Saclay - Ile-de-France
Alan Turing Bldg, Office 134
1 rue Honoré d'Estienne d'Orves
91120 Palaiseau
GPS:+48° 42' 52.11", +2° 12' 20.78"
Phone:+33 174 854 216
Email:steve.oudot[at]inria.fr (public key)

Research interests

  • topological data analysis
  • persistence theory: algebra, topology, algorithms, statistics, machine learning
  • manifold learning
  • mesh generation

Students

  • Julie Mordacq (since 2022)
  • Vadim Lebovici (2020-2023, co-advised with François Petit, now postdoc in the Mathematics Department at Oxford University)
  • Théo Lacombe (2017-2020, co-advised with Marco Cuturi, now Maître de Conférence at LIGM, Université Gustave Eiffel)
  • Nicolas Berkouk (2016-2020, now Postdoc at EPFL)
  • Elchanan Solomon (2016-2019, co-advised with Jeffrey Brock, now Research Assistant Professor at Duke University)
  • Jérémy Cochoy (2015-2018, now CTO at Symphonia)
  • Mathieu Carrière (2014-2017, now Research Scientist at Inria)
  • Mickaël Buchet (2011-2014, co-advised with Frédéric Chazal, now University Assistant at T.U. Graz)

Books
Steve Oudot. Persistence Theory: From Quiver Representations to Data Analysis. AMS Mathematical Surveys and Monographs, volume 209, 2015. [comments and corrections]

Note: you can download a watermarked pdf of the book (see pdf icon to the right). For copyright information and terms of use, see the terms page on the AMS website. 		  
F. Chazal, V. de Silva, M. Glisse, S. Oudot. The Structure and Stability of Persistence Modules. Springer Briefs in Mathematics, 2016.

Surveys
Steve Oudot and Elchanan Solomon. Inverse Problems in Topological Persistence. Abel Symposia, vol. 15, 2020.

Recent research projects and publications (click here for a comprehensive list)
Magnus Botnan, Steffen Oppermann, Steve Oudot and Luis Scoccola. On the bottleneck stability of rank decompositions of multi-parameter persistence modules. ArXiv preprint 2208.00300 [AT], July 2022.
Steve Oudot and Luis Scoccola. On the stability of multigraded Betti numbers and Hilbert functions. To appear in SIAM Journal on Applied Algebra and Geometry, 2023.
Magnus Botnan, Vadim Lebovici and Steve Oudot. Local characterizations for decomposability of 2-parameter persistence modules. Algebras and Representation Theory, February 2023.
Jacob Leygonie, Mathieu Carrière, Théo Lacombe and Steve Oudot. A Gradient Sampling Algorithm for Stratified Maps with Applications to Topological Data Analysis. To appear in Mathematical Programming, 2023.
Magnus Botnan, Steffen Oppermann and Steve Oudot. Signed Barcodes for Multi-Parameter Persistence via Rank Decompositions and Rank-Exact Resolutions. ArXiv preprint 2107.06800 [AT], July 2021. A short version appeared in Proc. Symposium on Computational Geometry, 2022.
Steve Oudot and Elchanan Solomon. Barcode Embeddings for Metric Graphs. Algebraic & Geometric Topology, 21(3):1209--1266, 2021.
Jacob Leygonie, Steve Oudot and Ulrike Tillmann. A Framework for Differential Calculus on Persistence Barcodes. Foundations of Computational Mathematics, 2021.
Magnus Botnan, Vadim Lebovici and Steve Oudot. On rectangle-decomposable 2-parameter persistence modules. Proc. Symposium on Computational Geometry, 2020. Full version in Discrete and Computational Geometry, 2022.

Teaching

 École polytechnique:
  • INF 442 -- Algorithms for data analysis in C++
  • INF 556 -- Topological Data Analysis
  • INF 631 -- Data Analysis: geometry and topology in arbitrary dimensions
Others:
  • Spring School in Luxembourg (March 2018): link
  • Summer School in TUM (July 2016): link
  • Spring School in La Marsa (April 2016): link