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 they coincide with combinatorial structures and also special configurations on polytopes:

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.

Uniformly Weighted Graphical Designs

Joint work with Rekha Thomas.
Preprint on ArXiv.
We characterize the existence of uniformly weighted graphical designs, and provide several families of graph that have, and do not have, such designs. Our results offer a polyhedral view of the structures that control the existence and cardinalities of these designs.

A broader theme in my research is connecting graphs to other mathematical structures. Alongside the connection between spectral graph theory and combinatorics above, I have also worked on the connections between certain graphs and flat surfaces:

Obtaining the Chamanara Surface from the van der Corput sequence

Joint work with Francois Clement and Max Horwitz.
Preprint on ArXiv.
We investigate a family of 4-regular graphs constructed from a sequence of real numbers, and construct embeddings into well-known surfaces: from the Kronecker sequence into the torus, and from the van der Corput sequence into the infinite-type Chamanara surface.

Conferences and Travels

Upcoming conferences I'm planning on attending

2027 Joint Mathematics Meetings, January 12 - 15, 2027, Chicago, IL.

You may have seen me at

Joint Boot Camp: Spectral Theory Beyond Graphs + Pseudorandomness and High-Dimensional Expansion, August 24 - September 4, 2026, Simons Institute for the Theory of Computing.
2026 SIAM Conference on Optimization, June 2 - 5, 2026, Edinburgh, UK.
2026 Joint Mathematics Meetings, January 4 - 7, 2026, Washington, DC.
5th Biennial Meeting of the Pacific Northwest Section of SIAM, October 3-5, 2025, UW.
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.
2025 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).