Research

I am interested in a mixture of geometry, probability, and dynamics, particularly in relation to hyperbolic manifolds of dimensions 2 and 3.

My current project with Lewis Bowen centers around the Benjamini-Schramm limit of random high-genus translation surfaces, sampled according to Masur-Veech measure. These Benjamini-Schramm limits characterize what it is like to live on a high genus translation surface; results about Benjamini-Schramm limits exist for various discrete objects, as well as Weil-Petersson random hyperbolic surfaces.

Publications

  1. Hunter A. Vallejos & James J. Nutaro & Kalyan S. Perumalla, 2018."An agent-based model of the observed distribution of wealth in the United States,"Journal of Economic Interaction and Coordination,Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 13(3), pages 641-656, October.

Conferences

  1. ISM Discovery School: Geometry and Spectra of Random Hyperbolic Surfaces (June 2023); University of Montreal.
  2. Dynamics, Rigidity, and Arithmetic in Hyperbolic Geometry (May 2023); ICERM.
  3. Graduate Mini-school in Groups, Dynamics, and Probability (May 2023); UT Austin.
  4. Texas Undergraduate Groups and Dynamics Conference (March 2023); UT Austin.
  5. SaltFlat: Mathematics research community in Teichmüller dynamics (January 2023); University of Utah.
  6. Nearly carbon neutral geometric topology conference (October 2022); Online.
  7. Graduate student concentration week on metric geometry (July 2022); Texas A&M.
  8. Graduate mini-school in groups and dynamics (July 2022); UT Austin.

Talks

  1. Random quasi-Fuchsian structures on surfaces (Spring 2023). UT Austin; Texas Undergraduate Groups and Dynamics Conference
  2. Billiards, translation surfaces, and introduction to ergodic theory (Spring 2023). Trinity University; Major's Seminar
  3. Local limits of high genus translation surfaces (Summer 2022). Texas A&M; Graduate Student Concentration Week on Metric Geometry.
  4. Benjamini-Schramm limits of high genus translation surfaces (Spring 2022). UT Austin; UT Groups & Dynamics Seminar (Candidacy Talk).

Informal Talks

  1. Counting curves on hyperbolic surfaces (Spring 2023). UT Austin; Junior Topology Seminar.
  2. Introduction to complex-analytic Teichmüller theory (Fall 2022). UT Austin; Junior Topology Seminar.
  3. Introduction to hyperbolic geometry (Fall 2022). UT Austin; UT Math Club.
  4. R-trees as limits of G-spaces (Spring 2022). UT Austin; Geometric Group Theory Learning Seminar.
  5. Siegel-Veech constants (Spring 2022). UT Austin; Junior Topology Seminar.
  6. Billiard flow and an introduction to ergodic theory (Fall 2021). UT Austin; UT Math Club.
  7. CAT(0) Spaces (Fall 2021). UT Austin; Geometric Group Theory Learning Seminar.
  8. The Planar Stochastic Hyperbolic Triangulation (Spring 2021). UT Austin; Junior Probability Seminar
  9. Randomly sampling half-translation surfaces (Spring 2021). UT Austin; Junior Geometry Seminar.
  10. Thurston's homeomorphism and an application to earthquake flow (Spring 2021). UT Austin; Junior Topology Seminar.
  11. Introduction to the mapping class group (Spring 2021). UT Austin; Mapping Class Group Learning Seminar.
  12. Translation surface basics (Fall 2020). UT Austin; Junior Topology Seminar.
  13. Conway's game of sprouts (Fall 2019). UT Austin; Sophex Seminar.
  14. An introduction to legendrian knot theory (Fall 2019). UT Austin; Junior Topology Seminar.
  15. TREE(3) and other big numbers (Fall 2019). UT Austin; Supervised Teaching Course.

Posters

  1. Polynomial Contact Homology on Legendrian Knots. Georgia Institute of Technology, UROP PURA Award. Under the mentorship of Caitlin Leverson.
  2. Stable Tame Isomorphisms of Legendrian Knots. Georgia Institute of Technology, Summer REU (2018).With DeVon Ingram and under the mentorship of Caitlin Leverson.
  3. On Augmentations of Legendrian Knots. Georgia Institute of Technology, Summer REU (2017).Under the mentorship of Caitlin Leverson.
  4. An agent-based modeal of the exponential-Pareto distribution of wealth. Oak Ridge National Laboratory, HERE Internship (2016). Under the mentorship of James J. Nutaro.
  5. Qualifying the Forecast Accuracy of Artificial Neural Networks on Stock Market Data. Oak Ridge National Laboratory, RAMS Internship (2015). Under the mentorship of James J. Nutaro.
  6. 1/f-Power Spectra and Fractals in the Heart: A Pedagogic View. Joint Oak Ridge High School - Oak Ridge National Laboratory, Math Thesis Program (2014-2015). Under the mentorship of Richard S. Ward.

Programs

  1. I built a program called polyCEDGA which computes the "polynomial" (contrast with "linearized") contact homology of the Chekanov-Eliashberg differential graded algebra of a Legendrian knot. It was built in Haskell. Email me for access to this program.