Introduction:

I am mostly interested in combinatorics (algebraic, geometric, topological), matroids and their variations, polyhedral geometry, and tropical geometry. But I am also branching out in related subjects including real algebraic geometry. I have been working on geometric objects associated with (oriented) matroids and their relation with tropical geometry, as well as Jacobians (also known as sandpile groups or critical groups) and the chip-firing game on graphs and their generalizations.

Preprints/In preparation:

1. Filtrations of the Tope Space of an Oriented Matroid
   With K. Shaw
   In preparation.


2. Extension-lifting Bijections for Oriented Matroids [arXiv link]
   With S. Backman and F. Santos
   Submitted.


3. The Amoeba Dimension of a Linear Space [arXiv link]
   With J. Draisma, S. Eggleston, R. Pendavingh, J. Rau
   Accepted by Proceedings of the American Mathematical Society.


4. The Critical Groups of Adinkras Up to 2-Rank of Cayley Graphs [arXiv link]
   Accepted by Electronic Journal of Combinatorics.


5. Sandpile Groups of Cayley Graphs of F_2^r [arXiv link]
   With J. Gao, J. Marx-Kuo, V. McDonald
   Submitted.


6. Oriented Matroids from Triangulations of Products of Simplices [arXiv link]
   With M. Celaya and G. Loho
   Accepted by Selecta Mathematica.

Journal Publications:

1. Eigenvalues and Critical Groups of Adinkras [arXiv link]
   With K. Iga, C. Klivans, and J. Kostiuk
   Advances in Applied Mathematics 143, Paper No. 102450, 2023.


2. Critical Groups of Strongly Regular Graphs and Their Generalizations [arXiv link]
   With K. Hung
   Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial 19, 95-109, 2022.


3. Patchworking Oriented Matroids [arXiv link]
   With M. Celaya and G. Loho
   Journal of the London Mathematical Society 106, 3545-3576, 2022.


4. The Dimension of an Amoeba [arXiv link]
   With J. Draisma and J. Rau
   Bulletin of the London Mathematical Society 52, 16-23, 2020.


5. On the Number of Circuit-cocircuit Reversal Classes of an Oriented Matroid [arXiv link]
   With E. Gioan
   Discrete Mathematics 342, 1056-1059, 2019.


6. Geometric Bijections for Regular Matroids, Zonotopes, and Ehrhart Theory [arXiv link]
   With S. Backman and M. Baker
   Forum of Mathematics, Sigma 7, e45, 37pp, 2019.


7. Geometric Bijections Between Spanning Trees and Break Divisors [arXiv link]
   Journal of Combinatorial Theory, Series A 152, 159-189, 2017.

Conference Papers:

1. Topological Bijections for Oriented Matroids [Link]
   With S. Backman and F. Santos
   Séminaire Lotharingien de Combinatoire 82B (2020), Art. 39, 12 pp.
   Accepted for contributed poster at FPSAC 2019.


2. Geometric Bijections for Regular Matroids, Zonotopes, and Ehrhart Theory [Link]
   With S. Backman and M. Baker
   Séminaire Lotharingien de Combinatoire 80B (2018), Art. 94, 11 pp.
   Accepted for contributed talk at FPSAC 2018.

PhD Thesis: