Galen Dorpalen-Barry Texas A&M

Research

I am interested in algebraic combinatorics, especially problems related to hyperplane arrangements, (oriented) matroids, posets, and related fields.

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    • ArXiv Preprints

Papers and Preprints

  1. Salvetti complexes for conditional oriented matroids, with Dan Dugger and Nick Proudfoot
    link to pdf arXiv:2507.06365 (2025) submitted
  2. The Ehrhart polynomial of a matroid specializes to the beta invariant, with Anastasia Chavez, Luis Ferroni, Fu Liu, Felipe Rincón, Andrés R. Vindas-Meléndez
    arXiv:2504.15518 (2025) submitted
  3. The geometry of zonotopal algebras I (cohomology of graphical configuration spaces), with Colin Crowley, André Henriques, and Nick Proudfoot
    link to pdf arXiv:2502.12768 (2025) submitted

  4. A Three-Regime Theorem for Flow-Firing, with Sarah Brauner, Selvi Kara, Caroline Klivans, and Lisa Schneider
    Electronic Journal of Combinatorics (2025)
     journal version, arXiv:2303.02526
  5. Equivariant cohomology and conditional oriented matroids, with Nicholas Proudfoot and Jidong Wang
    International Math Research Notices (2024)
     journal version, arXiv:2208.04855
  6. Shi Arrangements Restricted to Weyl Cones, with Christian Stump
    Annals of Combinatorics (2024)
     journal version, arXiv:2204.05829
  7. The Poincaré-Extended ab-index, with Joshua Maglione and Christian Stump
    Journal of the London Mathematical Society (2024)
     journal version, arXiv:2301.05904
    FPSAC abstract
  8. The Varchenko-Gel'fand Ring of a Cone
    Journal of Algebra (2023)
     journal version, arXiv:2104.02740/
  9. Filtering cohomology of ordinary and Lagrangian Grassmannians, with Vic Reiner and the students of the Polymath Jr. REU
    Involve (2022)
     journal version, arXiv:2011.03179
  10. A positivity phenomenon in Elser's Gaussian-cluster percolation model, with Cyrus Hettle, David C. Livingston, Jeremy L. Martin, George Nasr, Julianne Vega, and Hays Whitlatch
    Journal of Combinatorial Theory A (2021)
     journal version, arXiv:1905.11330/
  11. Whitney Numbers for Poset Cones, with Jang Soo Kim and Vic Reiner
    Order (2021)
     journal version, arXiv:1906.00036
  12. Enumerating Parking Completions Using Join and Split, with Ayomikun Adeniran, Steve Butler, Pamela E. Harris, Cyrus Hettle, Qingzhong Liang, Jeremy L. Martin, and Hayan Nam
    Electronic Journal of Combinatorics (2020)
     journal version, arXiv:1912.01688
Picture of an arrangement of the braid arrangement in three dimensions (with the linelity space marked in blue). A two-dimensional picture of the rank 2 affine Weyl arrangement with the dominant cone shaded and the braid and Shi arrangements hilighted in different colors. An arrangement of two planes in R^3 that intersect along a line.

Theses