Research
My current interests are in combinatorics and algebraic geometry.
My previous work includes algebraic combinatorics, mathematical modeling, and reinforcement learning.
Preprints
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2026
The Terwilliger algebra for the distance-regular graphs with valency three
About this paper
We study the Terwilliger algebras of the 13 distance-regular graphs of valency three, decomposing their standard modules into irreducible modules and determining the dimensions of the algebras.
Publications
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2025
Concrete billiard arrays of polynomial type and Leonard systems
About this paper
I construct concrete billiard arrays from the eigenspaces of a multiplicity-free linear map and describe how their boundaries relate to the split decompositions associated with a Leonard system. This work grew out of my senior honors thesis with Paul Terwilliger.
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2025
The Dynamics of Mood in Bipolar Disorder: How Mathematical Models Help Phenotype Individuals, Forecast Mood, and Clarify Underlying Mechanisms
About this paper
A review of mathematical approaches to describing mood dynamics in bipolar disorder, with an emphasis on how models can characterize individuals, forecast changes in mood, and help examine underlying mechanisms.
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2025
Integrating Local Learning into the Two-Stage Markov Task to Separate Model-Based from Model-Free Learning
About this paper
We propose a local-learning phase for the two-stage Markov task and evaluate it with simulations, aiming to better distinguish model-based from model-free learning.