Research:
- My first publication, On Some Nonrigid Unit Distance Patterns: https://rdcu.be/dqx5c. My coauthor and I study various problems related to the Unit Distance Problem in discrete geometry, especially questions of the form ‘How many times can a certain subgraph (a path, a cycle, a 3-regular graph) appear within a certain unit distance graph?’ Conducted through the Baruch REU in discrete mathematics.
- Some work on hyperbolic knot theory conducted through the SMALL REU: https://arxiv.org/abs/2209.04556 studies a generalization of the notion of hyperbolicity of knots to hyperbolic knotoids, and https://arxiv.org/pdf/2209.01922.pdf defines a further generalization of knotoids and extends various knot invariants to these new objects.
- These papers are to appear in the European Journal of Mathematics and Mathematical Proceedings of the Cambridge Philosophical Society respectively
- A report (formal paper still being written) on a connection between Young tableaux and simplicial complexes, conducted through the Twin Cities REU in algebra and combinatorics: https://www-users.cse.umn.edu/~reiner/REU/ REU2023notes/3_Jeu_de_Taquin_and_Simplicial_Complexes_final_report.pdf
- A report (formal paper still being written) on cluster monomials in graph Laurent phenomenon algebras. Our main result is that cluster monomials in linear Laurent phenomenon algebras form a linear basis, which is the analogue of a fact about cluster algebras. We also prove an analogue of a positivity conjecture for cluster algebras in some special cases. https://www-users.cse.umn.edu/~reiner/REU/ REU2023notes/5_Monomial_Positivity_and_Cluster_Algebras.pdf