Research

Broadly, I like to think about hyperbolic manifolds and the deformations they admit. For example, hyperbolic knot complements form a rich an interesting class of hyperbolic 3-manifolds, and there are higher dimensional analogues to consider as well. I like to think about special features of these manifolds, such as totally geodesic subcomplexes, as a way of obtaining deformations of the initial hyperbolic structure.

Currently, I am thinking about generalizations of bending deformations and how they can be used to address things like flexible manifolds and the Menasco-Reid conjecture.

Papers

Geometry & Topology

  1. Branched Bending in Finite-Volume Hyperbolic Manifolds, arXiv:2604.22004 (submitted)

Combinatorics

  1. (with T. Aguilar-Fraga, J. Elder, R. E. Garcia, K. P. Hadaway, P. E. Harris, K. J. Harry, I. B. Hogan, J. Johnson, J. Kretschmann, K. Lawson-Chavanu, J. C. M. Mori, D. Qui˜nonez, D. Tolson III, D. A. Williams II) Interval and ℓ-interval Rational Parking Functions, 2024. Discrete Mathematics and Theoretical Computer Science, vol. 26:1, Permutation Patterns 2023 #10
  2. (with Y. Aguillon, D. Alvarenga, P. E. Harris, S. Kotapati, J. Carlos Mart´ınez Mori, Z. Saylor, C. Tieu, D. A. Williams II) On Parking Functions and The Tower of Hanoi, 2022. The American Mathematical Monthly, 130:7, 618-624
  3. (with J. Ahn, C. Alar, B. Bjorkman, S. Butler, J. Carlson, A. Goodnight, H. Knox, M. C. Wigal) Ordered multiplicity inverse eigenvalue problem for graphs on six vertices, 2021. The Electronic Journal of Linear Algebra: Vol. 37 (2021), 316-358

Talk Slides

Branched Bending in Finite Volume Hyperbolic Manifolds

As seen at 3-manfiolds, groups, varieties workshop at Rutgers University-Newark, October 2025

Branched Bending and Cusped Hyperbolic Manifolds

As seen at AMS-UMI at UniPa, July 2024

Flexing and Branched Bending

As seen at GTA Philadelphia at Temple University, May 2024