My research lies at the intersection of applied topology, category theory, probabilistic models, and chemical reaction networks. Broadly speaking, I am interested in how abstract mathematical structure can clarify complex dynamical systems and provide principled ways to simplify them without losing the phenomena that matter.
A central theme of my current work is the study of chemical reaction network reduction. Chemical reaction networks are often too large to analyze directly, so reduction methods are essential. I am particularly interested in understanding these reductions through a structural and categorical lens: what information a reduction preserves, how different notions of reduction are related, and when reduction procedures can be transported across mathematical models. This perspective connects topology, algebraic structure, dynamics, and ideas from inference, and aims toward a more unified framework for reasoning about reaction networks.
More broadly, I am interested in the use of category-theoretic and topological methods in applied mathematics. These tools provide a language for comparing models, identifying shared structure, and organizing complicated systems in a way that can make both theory and computation more tractable.
Current work and papers
- Categorical Perspectives on Chemical Reaction Networks (with Justin Curry) This paper studies chemical reaction networks from a categorical point of view. In particular, it shows that topological reduction of a chemical reaction network can be understood through the stoichiometric functor into the arrow category of vector spaces, interprets the associated Schur complement as a categorical construction, and defines a reconstruction functor back to chemical reaction networks.
Surface growth and stochastic models
I have also worked on problems related to random surface growth and the topology of deposition models. In collaboration with Le Chen and Ian Ruau, I helped develop the Python package Tetris Random Deposition, which provides tools for simulating random deposition processes inspired by ballistic growth and related models from statistical physics.
These models are connected to questions of universality in surface growth, including phenomena associated with the Kardar--Parisi--Zhang (KPZ) framework. My interest in this area is both computational and mathematical: how discrete stochastic growth models behave, what large-scale features they exhibit, and how topology can help describe that behavior.