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
- 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
- ISM Discovery School: Geometry and Spectra of Random Hyperbolic Surfaces (June 2023); University of Montreal.
- Dynamics, Rigidity, and Arithmetic in Hyperbolic Geometry (May 2023); ICERM.
- Graduate Mini-school in Groups, Dynamics, and Probability (May 2023); UT Austin.
- Texas Undergraduate Groups and Dynamics Conference (March 2023); UT Austin.
- SaltFlat: Mathematics research community in Teichmüller dynamics (January 2023); University of Utah.
- Nearly carbon neutral geometric topology conference (October 2022); Online.
- Graduate student concentration week on metric geometry (July 2022); Texas A&M.
- Graduate mini-school in groups and dynamics (July 2022); UT Austin.
Talks
- Random quasi-Fuchsian structures on surfaces (Spring 2023). UT Austin; Texas Undergraduate Groups and Dynamics Conference
- Billiards, translation surfaces, and introduction to ergodic theory (Spring 2023). Trinity University; Major's Seminar
- Local limits of high genus translation surfaces (Summer 2022). Texas A&M; Graduate Student Concentration Week on Metric Geometry.
- Benjamini-Schramm limits of high genus translation surfaces (Spring 2022). UT Austin; UT Groups & Dynamics Seminar (Candidacy Talk).
Informal Talks
- Counting curves on hyperbolic surfaces (Spring 2023). UT Austin; Junior Topology Seminar.
- Introduction to complex-analytic Teichmüller theory (Fall 2022). UT Austin; Junior Topology Seminar.
- Introduction to hyperbolic geometry (Fall 2022). UT Austin; UT Math Club.
- R-trees as limits of G-spaces (Spring 2022). UT Austin; Geometric Group Theory Learning Seminar.
- Siegel-Veech constants (Spring 2022). UT Austin; Junior Topology Seminar.
- Billiard flow and an introduction to ergodic theory (Fall 2021). UT Austin; UT Math Club.
- CAT(0) Spaces (Fall 2021). UT Austin; Geometric Group Theory Learning Seminar.
- The Planar Stochastic Hyperbolic Triangulation (Spring 2021). UT Austin; Junior Probability Seminar
- Randomly sampling half-translation surfaces (Spring 2021). UT Austin; Junior Geometry Seminar.
- Thurston's homeomorphism and an application to earthquake flow (Spring 2021). UT Austin; Junior Topology Seminar.
- Introduction to the mapping class group (Spring 2021). UT Austin; Mapping Class Group Learning Seminar.
- Translation surface basics (Fall 2020). UT Austin; Junior Topology Seminar.
- Conway's game of sprouts (Fall 2019). UT Austin; Sophex Seminar.
- An introduction to legendrian knot theory (Fall 2019). UT Austin; Junior Topology Seminar.
- TREE(3) and other big numbers (Fall 2019). UT Austin; Supervised Teaching Course.
Posters
- Polynomial Contact Homology on Legendrian Knots. Georgia Institute of Technology, UROP PURA Award. Under the mentorship of Caitlin Leverson.
- Stable Tame Isomorphisms of Legendrian Knots. Georgia Institute of Technology, Summer REU (2018).With DeVon Ingram and under the mentorship of Caitlin Leverson.
- On Augmentations of Legendrian Knots. Georgia Institute of Technology, Summer REU (2017).Under the mentorship of Caitlin Leverson.
- 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.
- 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.
- 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
- 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.