I’m 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. I will be on the tenure track job market in the fall of 2025.
Research Interests
Differential Geometry, Minimal Surfaces, Hyperbolic Geometry, Dynamical Systems, Scalar Curvature, k-Surfaces, 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
- 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) – arXiv
- Minimal Submanifolds and Waists of Locally Symmetric Spaces (with Mikolaj Fraczyk) – pdf
- Finiteness of Totally Geodesic Hypersurfaces (with Simion Filip and David Fisher) – 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) – 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) – to appear in Annales scientifiques de l’École normale supérieure. 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- Area, Scalar Curvature, and Hyperbolic 3‑Manifolds – arXiv (superseded by “Minimal Surface Entropy and Average Area Ratio”).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:
- 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
Contact
Email: loweb24 [at] uchicago.edu
Office: Eckhart 408B