I'm interested in low dimensional topology, manifolds, knot theory, embedding spaces, and cobordisms.
Thesis
My thesis constructed 3-parameter families of embedded arcs in 4-manifolds. The main tool I use to study them are finite type invariants coming from Embedding Calculus. I also use notation inpired by cubical ω groupoids.
Other Papers
Another current research project deals with cobordism categories and TQFTs. We study the category of nested cobordisms between nested manifolds.
- Nested cobordisms, Cyl-objects and Temperley-Lieb algebras, with M. Calle, R. Hoekzema, L. Murray, N. Pacheco-Tallaj, C. Rovi, Mar 2024 [arxiv]
As an undergraduate, I worked on research projects on Hyperbolic knots, Schur functions, cyclic group actions on cyclic codes, and graph and matroid theory.
- Densities of Hyperbolic Cusp Invariants. Proceedings of the American Mathematical Society. Volume 146, Number 9, September 2018, Pages 4073-4089. [arxiv]
- Support Equalities Among Ribbon Schur Functions, with M. Gaetz, W. Hardt, The Electronic Journal of Combinatorics , Volume 26 Issue 3. Sep 2019 [arxiv]
- Cyclic Sieving for Cyclic Codes, with A. Mason, V. Reiner, Finite Fields and Their Applications. 73. Aug 2021 [arxiv]
Talks
- Homotopy groups and Embedding Spaces, Spring Topology and Dynamical Systems Conference. March 2023 [Slides]
- Support Inequalities among Ribbon Schur Functions. University of Minnesota Twin Cities. August 2017 [Slides]
- Cyclic Sieving of Dual Hamming Codes. University of Minnesota Twin Cities. August 2017 [Slides]
- Cusps of Hyperbolic Knots, Young Mathematicians Conference, August 2017. [Slides]
- Jacobians of Regular Matroids. Undergraduate Research Forum, Cornell University. July 2015. [Slides]