I am primarily interested in higher categorical structures and their applications to homotopy theory and type theory. In particular, I am currently focused on comparing how different abstract shape structures (such as simplicial, cubical, globular) describe higher categories and model univalent type theory. Other interests include categorical models of universal algebra, topos theory, pointless topology, and categorical structures in computer science, physics, and linguistics. 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.
- 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]