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My industry interests include (1) formal methods in software, infrastructure, and systems architecture; (2) machine learning & scientific computing; and (3) database systems. My principal aim in these domains is to responsibly integrate advanced mathematics into complex and critical systems.

My academic interests include (but are not limited to) (1) category theory, type theory, topos theory, and algebraic topology & geometry; and separately (2) machine learning and numerical methods. Some of my favorite studies live in the intersection of these two veins, e.g., neural sheaf diffusion and gene-ontology-based learning.

For my repository, see GitHub.

Slides

M.M., Formal Structures in Systems Architectures, presented at JMM 2026 Applied Category Theory Special Session.

For a slightly more introductory version presented to the UMN Math Club, see Designing Systems of Systems with Category Theory.

Paper

[1] M.M., Samantha Jarvis, Nelson Niu, Angeline Aguinaldo, Amanda Hicks, and Ian Levitt. Formal Structures in Systems Ontology towards Air Traffic Management Architectures. NASA Technical Memorandum, 2025. Report no. NASA/TM-20250010771. https://ntrs.nasa.gov/citations/20250010771

[2] On the Convergence Properties of the Deep JKO Scheme. Anticipated July 2026.