EDUARDO REYES
I am an Assistant Professor at the Mathematics Department of the Pontifical Catholic University of Chile (PUC).
I am interested in geometric group theory and its interactions with low-dimensional topology, geometric topology and dynamics. I like studying hyperbolic groups and their generalizations, groups acting on CAT(0) cube complexes, and deformation spaces of isometric actions.
Email: eduardoreyes + at + uc + dot + cl
Facultad de Matemáticas, Pontificia Universidad Católica de Chile
Edificio Rolando Chuaqui, Campus San Joaquín
Avda. Vicuña Mackenna 4860, Santiago, Chile
Office: 144
Facultad de Matemáticas, Pontificia Universidad Católica de Chile
Edificio Rolando Chuaqui, Campus San Joaquín
Avda. Vicuña Mackenna 4860, Santiago, Chile
Office: 144
RESEARCH
- Regularity of Manhattan manifolds and exact dimensionality for relatively Anosov groups (with Tianqi Wang), 2026. [arxiv]
- A geometric correspondence for reparameterizations of geodesic flows (with Stephen Cantrell and Dídac Martínez-Granado), 2026. [arxiv]
- Stably tangential strict hyperbolization (with Mauricio Bustamante and Stefano Riolo), 2026. [arxiv]
- The joint translation spectrum and Manhattan manifolds (with Stephen Cantrell and Cagri Sert), 2024, being comprehensively rewritten/extended. [arxiv]
- Approximating hyperbolic lattices by cubulations (with Nic Brody), 2024. [arxiv]
- Approximate marked length spectrum rigidity in coarse geometry (with Stephen Cantrell), 2026. [arxiv,journal]
- Marked length spectrum rigidity from rigidity on subsets (with Stephen Cantrell), 2025. [arxiv,journal]
- Rigidity phenomena and the statistical properties of group actions on CAT(0) cube complexes (with Stephen Cantrell), 2025. [arxiv,journal]
- Manhattan geodesics and the boundary of the space of metric structures on hyperbolic groups (with Stephen Cantrell), 2025. [arxiv,journal]
- On cubulated relatively hyperbolic groups, 2023. [arxiv,journal]
- The space of metric structures on hyperbolic groups, 2023. [arxiv,journal]
- A new inequality about matrix products and a Berger-Wang formula, 2020. [arxiv,journal]
- The Avalanche Principle and negative curvature, 2020. [arxiv,journal]
- Properties of sets of isometries of Gromov hyperbolic spaces, 2018. [arxiv,journal]
Preprints
Published
SOME SLIDES
- Complejos cúbicos y curvatura no positiva (in spanish). Coloquio UC. October 10, 2025.
- Green metrics on hyperbolic groups and reparameterizations of the geodesic flow. STCD. March 8, 2025.
- Approximating hyperbolic lattices by cubulations. World of Group Craft IV. September 9, 2024.
- Comparación estadística de acciones en complejos cúbicos CAT(0) (in spanish). Encuentro SOMACHI. December 19, 2023.
- Grupos, topología en dimensiones bajas, y curvatura no-positiva (in spanish). Colloquio Las Palmeras, Universidad de Chile. June 7, 2023.
- The space of metric structures on hyperbolic groups. Geometric Topology in New York, Columbia. June 3, 2023.
- The space of metric structures on hyperbolic groups (poster). Young Geometric Group Theory XI, Muenster. February 5, 2023.
- Continuity of Bowen-Margulis currents for hyperbolic groups. Workshop in Dynamical Systems and Related Topics, Penn State. November 6, 2022.
- Cubulated relatively hyperbolic groups. JMM, GGT Session. April 8, 2022.
- Matrix products inequalities, the Berger-Wang identity, and non-positive curvature. JMM, ILAS Session on Matrix Analysis and Applications. April 7, 2022.
STUDENTS
- Camila Pérez (MSc).
- Benjamín Maldonado (MSc).