My research projects

Persistence Theory
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. 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. ArXiv preprint 2107.06800 [AT], July 2021. A short version appeared in Proc. Symposium on Computational Geometry, 2022.
Magnus Botnan, Vadim Lebovici and Steve Oudot. Local characterizations for decomposability of 2-parameter persistence modules. Algebras and Representation Theory, February 2023.
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.
Clément Maria, Steve Oudot and Elchanan Solomon. Intrinsic Topological Transforms via the Distance Kernel Embedding. Proc. Symposium on Computational Geometry, 2020.
Jérémy Cochoy and Steve Y. Oudot. Decomposition of exact pfd persistence bimodules. Discrete and Computational Geometry, 63:255-293, Mar. 2020.
Nicolas Berkouk, Grégory Ginot and Steve Oudot. Level-sets persistence and sheaf theory. ArXiv preprint 1907.09759 [AT], Jul. 2019.
Ellen Gasparovic, Elizabeth Munch, Steve Oudot, Katharine Turner, Bei Wang and Yusu Wang. Intrinsic Interleaving Distance for Merge Trees. ArXiv preprint 1908.00063 [CG], Jul. 2019.
Michael Kerber, Michael Lesnick and Steve Oudot. Exact Computation of the Matching Distance on 2-Parameter Persistence Modules. Proc. Symposium on Computational Geometry, pages 46:1-15, 2019. Full version in Journal of Computational Geometry, 11(2), 2020.
Mathieu Carrière and Steve Y. Oudot. Local Equivalence and Intrinsic Metrics between Reeb Graphs. Proc. 33rd International Symposium on Computational Geometry (SoCG), 2017. Full version.
Clément Maria and Steve Y. Oudot. Computing Zigzag Persistent Cohomology. Arxiv preprint arXiv:1608.06039 [cs.CG].
Mathieu Carrière and Steve Y. Oudot. Structure and Stability of the 1-Dimensional Mapper. Proc. 32nd International Symposium on Computational Geometry (SoCG), 2016. Full version in J. Foundations of Computational Mathematics, 2018.
Clément Maria and Steve Y. Oudot. Zigzag Persistence via Reflections and Transpositions. Proc. ACM-SIAM Symposium on Discrete Algorithms (SODA), January 2015.   
S. Y. Oudot and D. R. Sheehy. Zigzag Zoology: Rips Zigzags for Homology Inference. Proc. 29th Annual Symposium on Computational Geometry, June 2013. Full version in J. Foundations of Computational Mathematics.   
F. Chazal, V. de Silva. S. Oudot. Persistence Stability for Geometric Complexes. Geometriae Dedicata, 173(1):193-214, 2014.
F. Chazal, D. Cohen-Steiner, M. Glisse, L. J. Guibas, S. Y. Oudot. Proximity of Persistence Modules and their Diagrams. Proc. 25th ACM Sympos. on Comput. Geom., pages 237-246, 2009 (full version).   

Applications in Topological Data Analysis
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.
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.
Rachel Jeitziner, Mathieu Carrière, Jacques Rougemont, Steve Oudot, Kathryn Hess, and Cathrin Brisken. Two-Tier Mapper: a user-independent clustering method for global gene expression analysis based on topology. Bioinformatics, Oxford University Press, Feb. 2019.
Théo Lacombe, Marco Cuturi and Steve Y. Oudot. Large Scale computation of Means and Clusters for Persistence Diagrams using Optimal Transport. Proc. 32nd Conference on Neural Information Processing Systems (NIPS), 2018.
Mathieu Carrière, Bertrand Michel and Steve Y. Oudot. Statistical Analysis and Parameter Selection for Mapper. Journal of Machine Learning Research, 19(12):1-39, 2018.
Thomas Bonis and Steve Y. Oudot. A fuzzy clustering algorithm for the mode-seeking framework. Pattern Recognition Letters, 102:37-43, 2018.
Mathieu Carrière, Marco Cuturi and Steve Oudot. Sliced Wasserstein Kernel for Persistence Diagrams. Proc. 34th International Conference on Machine Learning (ICML), 2017.
Thomas Bonis, Frédéric Chazal, Steve Oudot and Maksim Ovsjanikov. Persistence-based Pooling for Shape Pose Recognition. Proc. 6th International Workshop on Computational Topology in Image Context (CTIC), June 2016, Marseille.
Mathieu Carrière, Steve Y. Oudot, and Maksim Ovsjanikov. Stable Topological Signatures for Points on 3D Shapes. Proc. Sympos. on Geometry Processing, July 2015.
Mickaël Buchet, Frédéric Chazal, Tamal K. Dey, Fengtao Fan, Steve Y. Oudot, and Yusu Wang. Topological analysis of scalar fields with outliers. Proc. Sympos. on Computational Geometry, June 2015.   
M. Buchet and F. Chazal and S. Y. Oudot and D. R. Sheehy. Efficient and Robust Topological Data Analysis on Metric Spaces. Proc. ACM-SIAM Symposium on Discrete Algorithms (SODA), January 2015.
F. Chazal, L. J. Guibas, S. Y. Oudot, P. Skraba. Persistence-Based Clustering in Riemannian Manifolds. Proc. 27th Annual ACM Symposium on Computational Geometry, pages 97-106, 2011. Full version in Journal of the ACM, volume 60, issue 6, article 41.   
B. Hudson, G. L. Miller, S. Y. Oudot, D. R. Sheehy. Topological Inference via Meshing. Proc. 26th Annual ACM Symposium on Computational Geometry, pages 277-286, 2010.   
F. Chazal, D. Cohen-Steiner, L. J. Guibas, F. Mémoli, S. Y. Oudot. Gromov-Hausdorff Stable Signatures for Shapes using Persistence. Computer Graphics Forum (proc. SGP 2009), pages 1393-1403.   
F. Chazal, L. J. Guibas, S. Y. Oudot, P. Skraba. Analysis of Scalar Fields over Point Cloud Data. Proc. 19th ACM-SIAM Symposium on Discrete Algorithms, pp. 1021-1030, 2009. Full version in Discrete and Computational Geometry (DCG), 46(4):743--775, December 2011 (full version).   
F. Chazal, S. Y. Oudot. Towards Persistence-Based Reconstruction in Euclidean Spaces. Proc. 24th ACM Sympos. on Comput. Geom., pages 232-241, 2008 (full version).   

Other Topics in Data Science
Julian Le Deunf, Rudresh Mishra, Yves Pastol, Romain Billot and Steve Oudot. Seabed prediction from airborne topo-bathymetric lidar point cloud using machine learning approaches. IEEE OCEANS, 2021.

Reconstruction and Probing
J.-D. Boissonnat, R. Dyer, A. Ghosh, and S. Oudot. Only distances are required to reconstruct submanifolds. Computational Geometry: Theory and Applications, 66:32-67, 2017.
J. Gao, L. Guibas, S. Oudot, and Y. Wang. Geodesic Delaunay Triangulation and Witness Complex in the Plane. Proc. 19th ACM-SIAM Symposium on Discrete Algorithms, pages 571-580, 2008. Full version in Transactions on Algorithms (TALG), 6(4):67:1--67:47, August 2010 (full version).   
J.-D. Boissonnat, L. J. Guibas, and S. Y. Oudot. Manifold Reconstruction in Arbitrary Dimensions using Witness Complexes. Proc. 23rd ACM Sympos. on Comput. Geom., pages 194-203, 2007. Full version in Discrete and Computational Geometry, 42(1):37-70, 2009 (pdf).   
Steve Y. Oudot. On the Topology of the Restricted Delaunay Triangulation and Witness Complex in Higher Dimensions. Technical Report, Stanford University, November 2006. LANL arXiv:0803.1296v1 [cs.CG], http://arxiv.org/abs/0803.1296. Published in the full version of this paper.   
L. J. Guibas, S. Y. Oudot. Reconstruction using Witness Complexes. Proc. 18th ACM-SIAM Sympos. on Discrete Algorithms, pages 1076-1085, 2007. Full version in Discrete and Computational Geometry, 40(3):325-356, 2008 (pdf).   
J.-D. Boissonnat, L. J. Guibas, S. Y. Oudot. Learning Smooth Objects by Probing. Proc. 21st Annual Sympos. on Comput. Geom., pp. 198-207, 2005. Full version in Computational Geometry: Theory and Applications, 37:38-58, 2007 (pdf). Video available here.   

Mesh Generation
J.-D. Boissonnat, S. Y. Oudot. Provably Good Sampling and Meshing of Lipschitz Surfaces. Proc. 22nd Annual ACM Sympos. Comput. Geom., pages 337-346, 2006.   
S. Y. Oudot, L. Rineau, M. Yvinec. Meshing Volumes Bounded by Smooth Surfaces. Proc. 14th Internat. Meshing Roundtable, pp. 203-220, 2005. Full version in Engineering with Computers, 26(3):265-279, 2010 (pdf).   
J.-D. Boissonnat, S. Y. Oudot. Provably Good Sampling and Meshing of Surfaces. Graphical Models, volume 67, issue 5, pages 405-451, September 2005.   
J.-D. Boissonnat, S. Y. Oudot. An effective condition for sampling surfaces with guarantees. Proc. 9th ACM Sympos. on Solid Modeling and Applications, pp. 101-112, 2004.   
J.-D. Boissonnat, S. Y. Oudot. Provably Good Surface Sampling and Approximation. Proc. 1st Symposium on Geometry Processing (SGP), pp. 9-18, 2003.   

Proximity Queries
D. Arthur, S. Y. Oudot. Reverse Nearest Neighbors Search in High Dimensions using Locality-Sensitive Hashing. INRIA research report RR-7084, November 2010. arXiv:1011.4955v1 [cs.CG, cs.DS].