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.
My office is Eckhart 408B.
Email: loweb24 {at} uchicago.edu
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 situations.
Research Statement (Fall 2023)
Papers:
Minimal Submanifolds and Waists of Locally Symmetric Spaces (With Mikolaj Fraczyk ),
preprint available upon request.
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 version
Minimal Surface Entropy and Average Area Ratio (with André Neves), to appear in Journal of Differential Geometry.
Arxiv version
Area, Scalar Curvature, and Hyperbolic 3-Manifolds,
Arxiv version (Superseded by "Minimal Surface Entropy and Average Area Ratio." It gives simpler proofs of some of the results of that paper in a special case. Not for publication.)
Deformations of Totally Geodesic Foliations and Minimal Surfaces in Negatively Curved 3-Manifolds, Geometric and Functional Analysis volume 31, pages 895–929 (2021).
Journal Version, Arxiv version
Miscellaneous
I've also supervised students at the UChicago Mathematics REU.
Here are the papers they wrote for the program: