Research

Papers and Preprints

1. Tropical Toric Vector Bundles on Projective Space (with Sergio Cristancho, Caitlin Davis, Christopher Manon, Emma Pickard, and Mahrud Sayrafi)
   In preparation (~25 pp., expected December 2026).

2. Representations on the Top-Weight Cohomology of Smooth Toric Varieties
   In preparation (~20 pp., expected November 2026).

3. Augmented Singular Cohomology, Uniform Matroids, and Real-Rootedness (with Lorenzo Vecchi)
   Submitted. https://arxiv.org/abs/2609.15946

4. The Singular Cohomology Ring of a Uniform Matroid: Combinatorics and Lefschetz Properties
   Submitted. https://arxiv.org/abs/2606.07490

5. The Singular Cohomology Ring of a Matroid
   Submitted. https://arxiv.org/abs/2412.05732

6. The Unipotent Tropical Fundamental Group (with Eric Katz)
   J. London Math. Soc. (2026), 114:e70701. https://doi.org/10.1112/jlms.70701

Dissertation

Tor Groups of the Stanley–Reisner Ring of a Matroid
Most of the results from my dissertation appear in papers 4 and 5 above. Link to PDF.

From my Undergrad Days

1. Limit Sets and Internal Transitivity in Free Group Actions (with Jonathan Meddaugh)
   Preprint. https://arxiv.org/abs/1908.07382.

2. On 2-coloring the integers to forbid a distance and monochromatic translates of a triangle
   Geombinatorics 27 (2018), no.4, 137–146.