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My industry interests include (1) complex systems architecture and networked systems, particularily in distributed settings with concurrent, interdependent operations; (2) machine learning, specifically with (hyper)graph structured data; 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, somewhat,separately (2) machine learning and numerical methods. Some of my favorite studies live at the join of these two veins, e.g., neural sheaf diffusion and hypergraph representation learning.

You can find my GitHub here.

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 Convergence of the Lagrangian and Dynamic Deep JKO Schemes for High-Dimensional Nonlinear Wasserstein Gradient Flows. Anticipated July 2026.