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See my Papers and Events pages for the latest information.

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Introduction:

I am mostly interested in algebraic combinatorics, matroids (and variations thereof), polyhedral geometry, and tropical geometry, but I am also branching out in related subjects. 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.

Upcoming Activities:

Journal Publications/Preprints:

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

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

  3. Eigenvalues and Critical Groups of Adinkras [arXiv link]
    With K. Iga, C. Klivans, and J. Kostiuk
    Accepted by Advances in Applied Mathematics.

  4. 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.

  5. Oriented Matroids from Triangulations of Products of Simplices [arXiv link]
    With M. Celaya and G. Loho
    Submitted.

  6. Patchworking Oriented Matroids [arXiv link]
    With M. Celaya and G. Loho
    Accepted by Journal of the London Mathematical Society.

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

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

  9. 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.

  10. 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:

Geometric Bijections of Graphs and Regular Matroids.
I won the School of Math Best PhD Thesis Award at Georgia Tech.

Past (Invited) Research Visits:

Selected Presentations:

Organized Events: