Starting in 2027 I will be an assistant professor at Johns Hopkins University. In the fall of 2026 I will be at the Lodha Mathematical Sciences Institute for the Thematic Programme on Surface Group Representation and Analytic Group Theory. Before that, I was a Dickson Instructor and NSF Postdoc at the University of Chicago. Before that I was a graduate student at Princeton where my advisor was Fernando Coda Marques.
Research Interests
Differential Geometry, Minimal Surfaces, Hyperbolic Geometry, Dynamical Systems, Locally Symmetric Spaces. Much of my work is focused on rigidity phenomena, in a variety of different geometric settings.
Here are some surveys/notes that might be helpful if you want to learn more.
Papers
- Counting Minimal Lagrangians Via Mirzakhani Functions (with Fernando C. Marques and André Neves) – arXiv
- Asymptotically Geodesic Surfaces (with Fernando Al Assal) – pdf
- Existence of Minimal Surfaces in Infinite Volume Hyperbolic 3‑manifolds (with Baris Coskunuzer, Zeno Huang and Franco Vargas Pallete) – arXiv
- Rigidity of the hyperbolic marked energy spectrum and entropy for k‑surfaces (with Sebastien Alvarez and Graham Smith) – to appear in Journal de l'École Polytechnique. arXiv
- Minimal Submanifolds and Waists of Locally Symmetric Spaces (with Mikolaj Fraczyk) – pdf
- Finiteness of Totally Geodesic Hypersurfaces (with Simion Filip and David Fisher) – to appear in Duke Mathematical Journal. pdf
- Hyperbolic 3‑manifolds with uniform spectral gap for coclosed 1‑forms (with Amina Abdurrahman, Anshul Adve, Vikram Giri, and Jonathan Zung) – pdf
- Uniqueness and Non‑Uniqueness for the Asymptotic Plateau Problem in Hyperbolic Space (with Zeno Huang and Andrea Seppi) – to appear in Proceedings of the London Mathematical Society pdf
- Rigidity of Totally Geodesic Hypersurfaces in Negative Curvature – to appear in Commentarii Mathematici Helvetici. pdf
- Foliated Plateau Problems and Asymptotic Counting of Surface Subgroups (with Sebastien Alvarez and Graham Smith) – Annales scientifiques de l’École normale supérieure 58(3):607-663 (2025). arXiv
- Minimal Surface Entropy and Average Area Ratio (with André Neves) – Journal of Differential Geometry 130(2):443–475 (2025). pdf
- Beyond Almost Fuchsian Space (with Zeno Huang) – American Journal of Mathematics 147(2):329–353 (2025). arXiv, pdf
- Area, Scalar Curvature, and Hyperbolic 3‑Manifolds – arXiv (superseded by “Minimal Surface Entropy and Average Area Ratio”).
- Deformations of Totally Geodesic Foliations and Minimal Surfaces in Negatively Curved 3‑Manifolds – Geometric and Functional Analysis 31:895–929 (2021). journal version, pdf
Students
I have supervised a number of independent studies on topics ranging in analysis, geometry, and topology. If you think you might be interested in doing an independent study with me, don't hesitate to reach out.
I have also supervised students in the University of Chicago Mathematics REU program. Their project papers are below:
- Kaixu Zhang - Counting hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants - https://arxiv.org/abs/2508.13464
- Raman Aliakseyeu – Gromov's Betti Number Bound
- Yike He – Ricci Flow with Surgery
- Jacob Stump – An Introduction to Quasi‑Fuchsian Manifolds
- Gabriel Aguilar Perez – Comparison and Rigidity Statements in Geometry
- Annie Wei – Nash–Moser Iteration
- Richard Ye – Bourgain’s Embedding Theorem, Johnson–Lindenstrauss Lemma and the Sparsest Cut Problem
- Alex Hummels – Topological Equivalence of Linear Ordinary Differential Equations
Miscellaneous
CRM Montreal Minicourse Differential Geometry and Superrigidity
Contact
Email: loweb24 [at] uchicago.edu
Office: Eckhart 408B