Splitting Loops and Necklaces: Variants of the Square Peg Problem with Shujian Chen, Florian Frick, Sam Saloff-Coste, Linus Setiabrata and Hugh Thomas – Forum Math., Sigma, 8, e5 (2020). arXiv version

On the generalized Erdős–Kneser conjecture: proofs and reductions with Shuli Chen, Ethan Coldren, Florian Frick and Linus Setiabrata – J. Combin. Theory, Ser. B, 135 (2019): 227-237. arXiv version



Persistence Curves: Bounding Their Distances And Applications To Cancer Genomics with F. Javier Arusaga, Sergio Ardanza-Trevijano and Radmila Sazdanovic.

Polytope Order Polytopes with Doriann Albertin, Matthias Beck, Max Hlavacek, Leonardo Saud and Sampada Kolhatkar.

Categorification of the Chromatic Polynomial of a Hypergraph and Coloring Complexes – in preparation

Expository Notes and Papers

  • Here is a note which contains an explicit (i.e. with matrices) computation of chromatic graph homology.
  • Here is a note which explains why the Möbius band is a fiber bundle.
  • Here are the results of a machine learning project about the game Connect Four written with Dana Droz and John Darges for Kevin Flores’ Introduction to Machine Learning.
  • Here is an expository paper on Equivariant Cohomology and GKM Theory written for Ricky Liu’s Schubert Calculus.
  • Here is an expository paper on spectral sequences written by myself and Ezra Nance for Tye Lidman’s Algebraic Topology II.