Pronounshe/him

Department/College/UnitPhysical & Biological Sciences Division

TitleDr

AffiliationFaculty

Web SitePersonal

Primary Office LocationMcHenry Library
Office 4192

Mail StopMathematics Department

Research Interests

My research lies at the intersection of geometry and topology, with a focus on Riemannian manifolds with Ricci curvature bounded below and their non-smooth generalizations via optimal transport, known as RCD spaces. I am particularly interested in understanding the topological implications of curvature bounds through the lens of measured and equivariant Gromov–Hausdorff convergence. My work also draws on Alexandrov geometry, Ricci flow techniques, convex surface geometry, and sub-Riemannian geometry. I am especially interested in the following topics:

(1) fundamental groups of open manifolds with Ricci curvature bounded below,

(2) moduli spaces of non-smooth metrics,

(3) RCD spaces with constrained geometry.

Teaching Interests

• Differential geometry
• Complex Analysis
• Differential equations
• Topology

Selected Presentations

1. Sept 19, 2025, Topology, Ricci curvature, and volume growth, UNAM, DIVAGEO Seminar.
2. May 7, 2025, Moduli spaces of Alexandrov surfaces, UCSC, Geometry and Analysis seminar.
3. Oct 4, 2023, Ricci curvature lower bounds for singular spaces, UCSC, Geometry and Analysis seminar.
4. Feb 2, 2023, Moduli spaces of compact RCD(0,N)-structures, Durham University, Geometry and Topology seminar.
5. Dec 13, 2022, Moduli spaces of compact RCD(0,N)-structures, Hausdorff Center for Mathematics.

Selected Publications

• Navarro, D. (2025) Contractibility of moduli spaces of RCD(0,2)-structures. Annales de l'Institut Fourier, Online first, 47 p.
• Mondino, A., Navarro, D. (2023). Moduli spaces of compact RCD(0,N)-structures. Mathematische Annalen, 387(3–4), 1435–1480.
• Navarro, D., Pan, J. (2025). Universal non-CD of sub-Riemannian manifolds. arXiv preprint arXiv:2507.00471.
• Navarro, D., Pan, J., Zhu, X. (2024). On the topology of manifolds with nonnegative Ricci curvature and linear volume growth. arXiv preprint arXiv:2410.15488.
• Navarro, D., Moduli spaces of compact RCD structures (PhD Thesis 2023). University of Oxford.