Math Papers
Cellular Sheaves of Hilbert spaces
PhD thesis, 2025
My PhD thesis. This work introduces cellular sheaves of Hilbert spaces, a powerful infinite-dimensional generalization of weighted cellular sheaves. Applications include graph neural networks, opinion dynamics, and clock synchronization problems.
Hilbert Sheaf Machine Learning
In preparation, 2025
An application of cellular sheaves of Hilbert spaces to graph neural networks.
Categorical Linear Programming
In preparation, 2025
A new framework for linear programming via enriched category theory and the Chu construction.
Clearing Sections of Lattice Liability Networks
Preprint, 2025
A mathematical framework that unifies and extends the classical Eisenberg-Noe model of financial clearing in terms of networks of lattice-valued liabilities.
Lattice-Valued Bottleneck Duality
Preprint, 2025
A qualitative benchmark for the use of large language models in mathematics research. This work reformulates certain classical combinatorial duality theorems in the context of order lattices.
A combinatorial K-theory perspective on the Edge Reconstruction Conjecture in graph theory
Homology, Homotopy and Applications, 2025
A framework for abstract reconstruction problems using the K-theory of categories with covering families, which we then apply to reformulate the edge reconstruction conjecture in graph theory.
Philosophy Papers
Flash War
(In preparation) Chapter in Advancing Ethical and Legal Discussions of AI and Autonomy in Defense Systems
An exploration of the risk of rapid escalation on the battlefield posed by AI decision-making.
Defensive Autonomous Weapon Systems, Humanitarian Intervention, and the Golem of Prague
Preprint, 2024
An interdisciplinary paper that explores the ethics of "defensive" autonomous weapons systems through Yudl Rosenberg's rendition of the myth of the Golem of Prague. This paper is currently homeless, and we are looking for a suitable journal.