Papers
A - Data Geometry and Machine Learning
A7 "Understanding the dynamics of the frequency bias in neural networks" (with J. Molina, M. Courdurier, F. Sahli) https://arxiv.org/abs/2405.14957
A6 " Fisher Flow Matching for Generative Modeling over Discrete Data" (with O. Davis, J. Bose, S. Kessler, I. Ceylan, M. Bronstein) https://arxiv.org/abs/2405.14664
A5 "Long Tail Image Generation Through Feature Space Augmentation and Iterated Learning" (with R. Elberg and D. Parra) Extended abstract at LatinXI workshop at CVPR https://arxiv.org/abs/2405.01705
A4 "A Class of Topological Pseudodistances for Fast Comparison of Persistence Diagrams" (with R. Kindelan, N. Hirschfeld, M. Cerda) Oral contribution at AAAI24 https://arxiv.org/abs/2402.14489
A3 "Position Paper: Generalized grammar rules and structure-based generalization beyond classical equivariance for lexical tasks and transduction" (with S. Trivedi) https://arxiv.org/abs/2402.01629
A2 Three iterations of (d − 1)-WL test distinguish non isometric clouds of d-dimensional points (with P. Barcelo, V. Delle Rose, A. Kozachinskyi, C. Rojas) NeurIPS 2023 main conference arxiv.org/abs/2303.12853
A1 Approximation-Generalization Trade-offs under (Approximate) Group Equivariance (with S. Trivedi) NeurIPS 2023 main conference arxiv.org/abs/2305.17592
B - Chemistry and Biochemistry applications
B1 https://doi.org/10.3390/sym15122176 Steady State Kinetics for Enzymes with Multiple Binding Sites Upstream of the Catalytic Site (Osorio, M.I.; Petrache, M.; Salinas, D.G.; Valenzuela-Ibaceta, F.; González-Nilo, F.; Tiznado, W.; Pérez-Donoso, J.M.; Bravo, D.; Yáñez, O.) Symmetry 2023, 15, 2176.
C - Physics and Astrophysics applications
C1 https://arxiv.org/abs/2311.16306 The search for the lost attractor (Mario Pasquato, Syphax Haddad, Pierfrancesco Di Cintio, Alexandre Adam, Pablo Lemos, Noé Dia, Mircea Petrache, Ugo Niccolò Di Carlo, Alessandro Alberto Trani, Laurence Perreault-Levasseur, Yashar Hezaveh) -- Accepted by ML4PS workshop at NeurIPS 2023
D - Large particle systems with long-range interactions
D7 https://arxiv.org/abs/1908.09714 Crystallization for Coulomb and Riesz Interactions as a Consequence of the Cohn-Kumar Conjecture (with S. Serfaty) Proc. Amer. Math. Soc. 148 (2020), 3047-3057. DOI
D6 arXiv.org/abs/1902.08497 Unconstrained polarization (Chebyshev) problems: basic properties and Riesz kernel asymptotics (with D. Hardin and E. Saff) Potential Analysis 56, pages 21–64 (2022) DOI
D5 arxiv.org/abs/1707.07664 Equality of the Jellium and Uniform Electron Gas next-order asymptotic terms for Riesz potentials (with C. Cotar)
D4 arxiv.org/abs/1706.06008 Next-order asymptotic expansion for N-marginal optimal transport with Coulomb and Riesz costs (with C. Cotar) Advances in Mathematics, volume 344, pages 137-233, 21 February 2019. DOI (15 minute talk about this paper available here )
D3 arxiv.org/abs/1609.03849 Equidistribution of jellium energy for Coulomb and Riesz interactions (with S. Rota-Nodari) Constructive Approximation, volume 47, issue 1, pages 163-210, February 2018. DOI
D2 arxiv.org/abs/1507.00782 Decorrelation as an avatar of convexity
D1 arxiv.org/abs/1409.7534 Next-order asymptotics and renormalized energy for Riesz interactions (with S. Serfaty) Journ. Inst. Math. Jussieu, Volume 16, Issue 3, June 2017, Pages 501-569. DOI
E - Rigidity, crystallization and regular structures
E8 arxiv.org/pdf/2308.07446 Effective recovery of Fourier spectra and spectral approximation by finite groups (with Rodolfo Viera)
E7 arxiv.org/abs/2112.11613 Almost sure recovery in quasi-periodic structures (with Rodolfo Viera) J Stat Phys 190, 39 (2023). https://doi.org/10.1007/s10955-022-03059-2
E6 arxiv.org/abs/2101.11977 Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings (with Giacomo Del Nin) Calc. Var. 61, 226 (2022). https://doi.org/10.1007/s00526-022-02318-0
E5 arxiv.org/abs/2012.11039 Sharp discrete isoperimetric inequalities in periodic graphs via discrete PDE and Semidiscrete Optimal Transport (with Matias Gomez)
E4 arxiv.org/abs/1907.06105 Crystallization to the square lattice for a two-body potential (with L. Bétermin and L. De Luca ) Archive for Rational Mechanics and Analysis 240 (2), 987-1053 DOI (Popularization interview in French about the paper available here)
E3 arxiv.org/abs/1905.09601 Classification of uniformly distributed measures of dimension 1 in general codimension (with P. Laurain), Asian J. Math 25 (4), 565 – 578 DOI.
E2 arxiv.org/abs/1806.02233 Optimal and non-optimal lattices for non-completely monotone interaction potentials (with L. Bétermin), Analysis and Mathematical Physics, volume 9, pages 2033–2073 (2019). https://doi.org/10.1007/s13324-019-00299-6
E1 arxiv.org/abs/1607.08716 Dimension reduction techniques for theta functions on lattices (with L. Bétermin) Journal of Mathematical Physics 58, 071902 (2017). DOI: http://dx.doi.org/10.1063/1.4995401
F - Fluid dynamics
F1 arxiv.org/abs/1710.09903 The Navier-slip thin-film equation for 3D fluid films: existence and uniqueness (with M. Gnann), JDE, vol. 265, n. 11 (2018), 5832-5958. https://doi.org/10.1016/j.jde.2018.07.015
G - Topological singularities in Yang-Mills theory, Nonlinear Sobolev spaces
Partial regularity for weak connections in high dimensions, in preparation (with T. Riviere)
G9 arxiv.org/abs/1812.04432 The Space of Weak Connections in High Dimensions (with T. Rivière)
G8 arxiv.org/abs/1306.2010 The resolution of the Yang-Mills Plateau problem in super-critical dimension (with T. Rivière) Advances in Mathematics, Volume 316, 20 August 2017, Pages 469-540, DOI
G7 arxiv.org/abs/1508.07813 Controlled singular extension of critical trace Sobolev maps from spheres to compact manifolds (with J. Van Schaftingen) Int. Math. Res. Not., 2017 (12), Pages 3647-3683, DOI
G6 arxiv.org/abs/1306.6763 A singular radial connection over B^5 minimizing the Yang-Mills energy Calc. Var. and PDE, 54 (2015) no.1, 631-642. DOI
G5 arxiv.org/abs/1302.5659 Global gauges and global extensions in optimal spaces (with T. Rivière) Analysis and PDE, 7 (2014), No. 8, 1851–1899. DOI
G4 arxiv.org/abs/1204.0209 Interior partial regularity for minimal L^p-vectorfields with integer fluxes Ann. S.N.S. Pisa Cl. Sci., Vol. XIV (2015), issue 4, 1119-1156. DOI
G3 arxiv.org/abs/1204.0175 Notes on a slice distance for sigular L^p-bundles Journ. Funct. Anal., 267 (2014), no. 2, 405–427. DOI
G2 arxiv.org/abs/1007.0681 An integrability result for L^p-vectorfields in the plane Adv. Calc. Var., 6 (2013), no. 3, 299–319. DOI
G1 arxiv.org/abs/1007.0668 Weak closure of singular abelian L^p-bundles in 3-dimensions (with T. Rivière) Geom. Funct. Anal. 21 (2011), 1419-1442. DOI
H - Optimal transport and currents
H6 arxiv.org/abs/2401.07880 Existence and uniqueness of Monge minimizers for a Multi-marginal Optimal Transport problem with intermolecular interactions cost (with A. Gerolin, A. Vargas-Jimenez) Accepted in Journal of Convex Analysis
H5 arxiv.org/pdf/2309.08677 Optimal Quantization with Branched Optimal Transport distances (with Paul Pegon)
H4 arxiv.org/abs/1903.09817 Cyclically monotone non-optimal N-marginal transport plans and Smirnov-type decompositions for N-flows ESAIM: COCV vol. 26, article number 120 (2020). DOI
H3 arxiv.org/abs/1707.03485 Coefficient groups inducing nonbranched optimal transport (with R. Züst), Zeitschrift fur Analysis und ihre Anwendungen, vol. 37, n. 4 (2018), 389-416. DOI
H2 arxiv.org/abs/1410.0062 Matchings in metric spaces, the dual problem and calibrations modulo 2 (with R. Züst), New York Journal of Mathematics http://nyjm.albany.edu/j/2016/22-57.html.
H1 arxiv.org/abs/1211.6677 A continuous model of transportation revisited (with L. Brasco) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov, Journ. Math. Sci., 196 (2014), no. 2, 119-137. DOI
I - Mean-field equations for higher-order laplacians
I2 arxiv.org/abs/1001.5231 Existence of solutions to a higher dimensional mean-field equation on manifolds (with L. Martinazzi) Manuscripta Math. 133 (2010), 115-130. DOI
I1 arxiv.org/abs/0904.3290 Asymptotics and quantization for a mean-field equation of higher order (with L. Martinazzi) Comm. Partial Differential equations 35 (2010), 1-22. , DOI
Theses
PhD thesis: Weak bundle structures and a variational approach to Yang-Mills Lagrangians in supercritical dimensions Download
Master's degree thesis: Differential inclusions and the Euler equation Download