Research
My research interests include combinatorics, spectral graph theory, discrete geometry and optimization. Recently, I've been working to understand graphical designs, and have proved results about them coinciding with combinatorial structures:
Graphical Designs Find Combinatorial Structures
- Joint work with Stefan Steinerberger and Rekha Thomas.
- Preprint on ArXiv.
- We show that in highly-structured graphs, graphical designs can coincide with highly structured and well-known combinatorial objects. These connections allow tools from spectral graph theory to bear on these combinatorial objects.
Conferences and Travels
Upcoming conferences I'm planning on attending
- 5th Biennial Meeting of the Pacific Northwest Section of SIAM, October 3-5, 2025, UW.
- Joint Mathematics Meetings, January 4 - 7, 2026, Washington, DC.
You may have seen me at
- Gender Equity in the Mathematical Study (GEMS) of Optimization, August 3-9, 2025, UBC Okanogan (attended virtually).
- SIAM Conference on Applied Algebraic Geometry (AG25), July 7-11, 2025, University of Wisconsin, Madison.
- 2025 Spring Western AMS Sectional Meeting, May 3-4, 2025, California Polytechnic, SLO.
- Cascade Lectures in Combinatorics, eighth meeting, March 8, 2025, UW.
- Oregon Number Theory Days 2025, March 1-2, 2025, Oregon State University.
- Joint Mathematics Meetings, January 8 - 11, 2025, Seattle, WA.
- Field of Dreams, November 10-12, 2024, Atlanta, GA.
- BRIDGES 2024, July 10-12, 2024, University of Utah.
- Roots of Unity 2024, June 10-14, 2024, ICERM.
- AWS 2024: Abelian Varieties, March 2-6, 2024, University of Arizona.
Past Research
My undergraduate research experiences were a little far from my current interests, venturing into the computational aspects of translation surfaces and the cognitive science of language. Some of this work has been published in the following papers:
Computing Periodic Points on Veech Surfaces
- Joint work with Samuel Everett, Sam Freedman and Destine Lee.
- Published in Geometriae Dedicata 217.4 (2023): 66.
- We present an algorithm to find the periodic points (with finite orbit under the affine automorphism group) of any non-square-tiled Veech surface. This provides a new proof of the finiteness of periodic points.
Event Knowledge in Large Language Models: The Gap Between the Impossible and the Unlikely
- Joint work with Carina Kauf, Anna A. Ivanova, Giulia Rambelli, Emmanuele Chersoni, Jingyuan Selena She, Evelina Fedorenko and Alessandro Lenci.
- Published in Cognitive Science 47, no. 11 (2023): e13386.
- We studied whether LLMs can leverage word co-occurence patterns to acquire knowledge of common events. We found that they almost always assign a higher likelihood to possible versus impossible events (The teacher bought the laptop vs. The laptop bought the teacher), but they showed less consistent preferences for likely versus unlikely events (The nanny tutored the boy vs. The boy tutored the nanny).