Research

Publications

Preprints

1. Joe Barton, Tobias Beran, Mauricio Che, Sebastian Gieger, Jona Röhrig, Felix Rott. A Splitting Theorem for non-positively curved Lorentzian spaces. arXiv:2601.14058.

2. Andrés Ahumada Gómez, Mauricio Che, Manuel Cuerno. Metric pairs and tuples in theory and applications. arXiv:2505.12735.

3. Mauricio Che. Optimal partial transport for metric pairs. arXiv:2406.17674. 

Published

1. Mauricio Che, Raquel Perales, Christina Sormani. Gromov's Compactness Theorem for the Intrinsic Timed-Hausdorff Distance. Differential Geometry and its Applications 103, 2026. DOI:10.1016/j.difgeo.2026.102364.

2. Mauricio Che, Fernando Galaz-García, Martin Kerin, Jaime Santos-Rodríguez. Isometric Rigidity of Metric Constructions with respect to Wasserstein Spaces.  Journal of Functional Analysis 290 (11), 2026. DOI:10.1016/j.jfa.2026.111415.

3. Mauricio Che, Fernando Galaz-García, Luis Guijarro, Ingrid Amaranta Membrillo Solis. Metric Geometry of Spaces of Persistence Diagrams. Journal of Applied and Computational Topology, 2024. DOI:10.1007/s41468-024-00189-2.

4. Mauricio Che, Fernando Galaz-García, Luis Guijarro, Ingrid Amaranta Membrillo Solis, Motiejus Valiunas. Basic Metric Geometry of the Bottleneck Distance. Proc. Amer. Math. Soc. 152, 3575-3591, 2024. DOI:10.1090/proc/16776.

5. Andrés Ahumada Gómez, Mauricio Che. Gromov-Hausdorff convergence of metric pairs and metric tuples (2023). Differential Geometry and its Applications 94, Paper No. 102135, 2024. DOI:10.1016/j.difgeo.2024.102135.

6. Mauricio Che, Jesús Núñez-Zimbrón. Ball covering property and number of ends of CD spaces with non-negative curvature outside a compact set, Archiv der Mathematik 119, 213–224, 2022. DOI:10.1007/s00013-022-01753-x.

PhD thesis

• Mauricio Che. Geometry of generalised spaces of persistence diagrams and optimal partial transport for metric pairs. PhD thesis, Durham University, 2024. Durham e-Theses.

Expository

1. Mauricio Che. El problema de Erdős-Perelman, Miscelánea Matemática, 71, 63-81, 2021. DOI: 10.47234/mm.7107.

2. Mauricio Che. On the number of ends of an Alexandrov space, Abstraction & Application, 27, 66-88, 2020. (link)

3. Mauricio Che, Didier Solis Gamboa. Espacios homogéneos de curvatura seccional positiva, Abstraction & Application, 26, 13-31, 2019. (link)

Interdisciplinary

1. Brian K. S. Isaac-Medina, Mauricio Che, Yona F. A. Gaus, Samet Akcay, Toby P. Breckon. FEVER-OOD: Free Energy Vulnerability Elimination for Robust Out-of-Distribution Detection. In: Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pp. 4529-4538. October, 2025. 

Talks

Upcoming talks

1. Gromov's compactness theorem for timed-metric spaces, at Research Seminar Mathematical Relativity, University of Hamburg, Germany (2026).

2. TBD, Seminario Interinstitucional en Geometría UADY-UNAM, hybrid seminar (2026)

Selected talks

1. Gromov's compactness theorem for timed-metric spaces, at Convergence or Scalar Curvature (COSC), online seminar (2026). 

2. Wasserstein spaces & Isometric rigidity at Optimal transport and metric geometry across stuctures, EPFL, Switzerland (2025).

3. Spaces of Persistence Diagrams and Beyond, Seminar of Department of Quantitative Methods & Mathematics at CUNEF Universidad, Spain (2025).

4. Spaces of Persistence Diagrams and Optimal Partial Transport, Seminar in Geometry and Statistics, Vrije Universiteit Brussel, Belgium (2025).

5. Optimal partial transport and non-negatively curved Alexandrov spaces, Applied Topology Seminar, University of Oxford, UK (2025).

6. Isometric rigidity with respect to Wasserstein spaces, AG Geometrie, Karlsruhe Institute of Technology, Germany (2025).

7. Isometric Rigidity and Flexibility of Wasserstein Spaces at 1st UK Metric Geometry Research Network Meeting, Cardiff University, UK (2024).

8. Isometric Rigidity and Flexibility of Wasserstein Spaces at Junior Analysis & Probability Seminar, University of Warwick, UK (2023).

9. Metric geometry of spaces of persistence diagrams at AMS MSRI Special Session: Differential & Metric Geometry in JMM, USA (2023).

10. Gromov-Hausdorff for metric pairs and tuples at Técnicas Modernas en Geometría Riemanniana, UNAM, online (2023).

11. Sobre los finales de espacios con curvatura no negativa fuera de un compacto at Técnicas Modernas en Geometría Riemanniana & Coloquio de Geometría, UADY, online (2022).

12. El teorema de Gauss-Bonnet-Chern at Dialogos Virtuales de Análisis y Geometría, UNAM, online seminar (2022).

13. Metric geometry of spaces of persistence diagrams at 8th Mexican Workshop on Applied Geometry and Topology, CIMAT, online (2022).

14. Cheeger-Gromoll splitting theorem and some generalizations at RCD spaces: splitting theorems and applications, UNAM, online (2021).