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.
- Shape Independent Category Theory and Enrichment. Category Theory OctoberFest, Johns Hopkins University, October 2019. [Slides]
- 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]
- Density Constructions for Hyperbolic Link Invariants. Olivetti Club, Cornell University, October 2017 and Graduate Student Seminar, Brandeis University, February 2017. [Slides]
- The Geometry of Knots (Cusp Densities of Links). MathFest, August 2016. [Slides]
- Cusp Density: Dense or Knot?. Unknot III Conference, August 2016. [Slides]
- Non-Standard Interactions and Neutrino Oscillations in Core-Collapse Supernovae. Astrophysics Group, Brandeis University, October 2014. [Slides]
- Neutrinos and the Unknown. North Carolina Museum of Natural Sciences, July 2014. [Slides]
- Cusp Invariants: Dense or Knot?. Summer Research Symposium, Williams College, August 2016. [Poster]
- Non-Standard Interactions and Neutrino Oscillations in Core-Collapse Supernovae II. NCSU Undergraduate Research Symposium, July 2014. [Poster]
- Non-Standard Interactions and Neutrino Oscillations in Core-Collapse Supernovae I. UNC/NCSU CAP/URCA Joint Physics Poster Session, July 2014. [Poster]