Steve Oudot

Directeur de Recherche (Senior Researcher), head of the GeomeriX group, Inria
Professeur Chargé de Cours (Adjunct Professor), 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

  • persistence theory and its connections to homological algebra, representation theory, and sheaf theory
  • topological data analysis and its connections to statistics, non-smooth optimization, and machine learning
  • multimodal time series analysis
  • manifold learning, sampling and reconstruction

Students

  • Jingyi Li (since 2023)
  • Julie Mordacq (since 2022, co-advised with Vicky Kalogeiton)
  • 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 Data Analyst at the CNIL)
  • Elchanan Solomon (2016-2019, co-advised with Jeffrey Brock, now Lead Scientist at Deep Detection)
  • Jérémy Cochoy (2015-2018, now CEO at Redstone Solution OÜ)
  • Mathieu Carrière (2014-2017, now Chargé de Recherche at Inria)
  • Mickaël Buchet (2011-2014, co-advised with Frédéric Chazal, now Data Consultant at Polyconseil)

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. Advances in Mathematics, 451:109780, 2024.
Steve Oudot and Luis Scoccola. On the stability of multigraded Betti numbers and Hilbert functions. SIAM Journal on Applied Algebra and Geometry, 8(1):54--88, 2024.
Magnus Botnan, Steffen Oppermann and Steve Oudot. Signed Barcodes for Multi-Parameter Persistence via Rank Decompositions and Rank-Exact Resolutions. To appear in Foundations of Computational Mathematics. A short version appeared in Proc. Symposium on Computational Geometry, 2022.
Vadim Lebovici, Jan-Paul Lerch and Steve Oudot. Local Characterization of Block-Decomposability for Multiparameter Persistence Modules. ArXiv preprint arXiv:2402.16624 [RT], June 2024.
Luis Scoccola, Siddharth Setlur, David Loiseaux, Mathieu Carrière and Steve Oudot. Differentiability and Optimization of Multiparameter Persistent Homology. Proc. 41st International Conference on Machine Learning (ICML), 2024.
Soham Mukherjee, Shreyas N. Samaga, Cheng Xin, Steve Oudot and Tamal K. Dey. D-GRIL: End-to-End Topological Learning with 2-parameter Persistence. ArXiv preprint 2406.07100 [LG], June 2024.
Julie Mordacq, Leo Milecki, Maria Vakalopoulou, Steve Oudot and Vicky Kalogeiton. ADAPT: Multimodal Learning for Detecting Physiological Changes under Missing Modalities. Proc. Medical Imaging with Deep Learning (MIDL), 2024.
Vadim Lebovici, Steve Oudot and Hugo Passe. Efficient computation of topological integral transforms. Proc. Symposium on Experimental Algorithms (SEA), 2024.
David Loiseaux, Luis Scoccola, Mathieu Carrière, Magnus Botnan and Steve Oudot. Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures. Proc. 37th Conference on Neural Information Processing Systems (NeurIPS), 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. Mathematical Programming, 202:199--239, 2023.

Teaching

 École polytechnique:
  • INF 442 -- Algorithms for data analysis in C++
  • INF 556 -- Topological Data Analysis
  • MPRI -- Computational Geometry and Topology
Others:
  • Spring School in Luxembourg (March 2018): link
  • Summer School in TUM (July 2016): link
  • Spring School in La Marsa (April 2016): link