I am primarily interested in different kinds of higher categorical structures and how they relate to each other, and am currently focused on how techniques from universal algebra can be used to describe different sorts of higher categories. When I say "higher categories" I mean any structure involving collections of cells in various shapes and operations for composing certain kinds of diagrams of those cells into a single cell. For instance, n-categories are algebraic structures on n-globular sets, and n-tuple categories are algebraic structures on n-cubical sets.

I am also interested in applying (sometimes higher) categorical techniques to other fields such as homotopy theory, K-theory, type theory, probability, and rewriting theory.

As an undergrad I did research in polyhedral decompositions of manifolds, hyperbolic knot theory, formal languages for concurrent processes, and computational astrophysics of plasma jets and supernova neutrinos.

Talks

Undergraduate Research

Papers

  • Densities of Hyperbolic Cusp Invariants. Proceedings of the American Mathematical Society. Volume 146, Number 9, September 2018, Pages 4073–4089. [PDF] [arXiv]

  • specgen: A Tool for Modeling Statecharts in CSP. Nasa Formal Methods 282, 2017.

  • Nonstandard Neutrino Interactions In Supernovae. Physical Review D 94, 093007, 2016. [PDF] [arXiv]

Talks

Posters



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