David Perkinson — Research

CV

Curriculum Vitae (2026)

Publications

2025Cycle systems, coparking functions, and h-vectors of matroids, with Scott Corry, Anton Dochtermann, Solis McClain, and Lixing Yi
2023Counting weighted maximal chains in the circular Bruhat order, with Gopal Goel and Olivia McGough. Journal of Combinatorial Theory, Series A 195, paper 105709
2022Simplicial Dollar Game, with Jesse Kim. Electronic Journal of Combinatorics
2020Enumerating linear systems on graphs, with Sarah Brauner and Forrest Glebe. Mathematische Zeitschrift
2019Critical groups of iterated cones, with Gopal Goel. Linear Algebra and its Applications
2018Divisors and Sandpiles, with Scott Corry. AMS textbook
2017
G-parking functions and tree inversions, with Qiaoyu Yang and Kuai Yu. Combinatorica (arXiv)
- Related: Parking functions and tree inversions revisited, by P. Gaydarov and S. Hopkins, Advances in Applied Mathematics, 2016
2016
Bigraphical arrangements, with Sam Hopkins. Transactions of the AMS
- Related: Multigraph Hyperplane Arrangements and Parking Functions, by M. Mazin, 2014
2015Sandpiles and Dominos, with L. Florescu, D. Morar, N. Salter, and T. Xu. Electronic Journal of Combinatorics
2015Sandpiles, spanning trees, and plane duality, with M. Chan, D. Glass, M. Macauley, C. Werner, and Q. Yang. SIAM Journal on Discrete Mathematics
2013Primer for the algebraic geometry of sandpiles, with J. Perlman and J. Wilmes. Tropical and Non-Archimedean Geometry, Contemp. Math. 605, AMS
2012Orientations, semiorders, arrangements, and parking functions, with S. Hopkins. Electronic Journal of Combinatorics 19(4)
2011A Note on the Critical Group of a Line Graph, with N. Salter and T. Xu. Electronic Journal of Combinatorics 18(1)
2011Frobenius polytopes, with J. Collins
2006Permutation Polytopes and Indecomposable Elements in Permutation Groups, with R. Guralnick. Journal of Combinatorial Theory, Series A 113(7)
2004Some facets of the polytope of even permutation matrices, with J. Hood. Linear Algebra and its Applications 381
2001Eight Lectures on Monomial Ideals, with E. Miller. Queens Papers in Pure and Applied Mathematics 120
2000Inflections of toric varieties. Michigan Math. J. 48
1996Principal parts of line bundles on toric varieties. Compositio Mathematica 104
1995Curves in Grassmannians. Transactions of the AMS

Book

Divisors and Sandpiles (with Scott Corry), AMS Student Mathematical Library Series. An introduction to chip-firing, the Riemann–Roch theorem for graphs, and the abelian sandpile model.

Lecture Notes

Software

I am a developer for SageMath, the open-source mathematical software system.

Presentations

Cycle systems, coparking functions, and h-vectors of matroids, Brown University, March 2026
Sandpiles and dominos, Mathematics Teacher-Scholar Symposium, Reed College, May 2021
Simplicial Dollar Game, SIAM PNW Conference, October 2019
A Chip-Firing Miscellany, Portland State University, May 2019
Enumerating Linear Systems on Graphs, Cornell University, April 2019
Enumerating Linear Systems on Graphs, MIT, November 2018
Enumerating Linear Systems on Graphs, Yale University, November 2018
The Threshold Density Theorem, Yale University, November 2018
The Threshold Density Theorem, Texas State University, San Marcos, October 2018
Enumerating Linear Systems on Graphs, Texas State University, San Marcos, October 2018
Sandpiles, spanning trees, and plane duality, JMM Seattle, January 2016
Sandpiles in Sage, BIRS-CMO Sandpiles workshop, Oaxaca, Mexico, November 2015
Tree inversions and parking functions, AMS Western Sectional Meeting, Las Vegas, April 2015
Sandpiles and Dominos, Claremont Colleges Mathematics Colloquia, February 2015
Tree inversions and parking functions, University of Idaho, October 2014
Tree inversions and parking functions, MathFest, August 2014
Sandpiles and Dominos, McDougal Lecture in Mathematics, Lawrence University, May 2014
The mathematics of juggling: theory and applications, African Institute for Mathematical Sciences, Cameroon, January 2014
Bigraphical arrangements, PEAKS 2013, Haus Bergkranz, Austria, March 2013
Invited speaker, Mathematical Congress of the Americas, Guanajuato, Mexico, August 2013
Project NExT panelist, Keeping Your Research Alive, Willamette University, April 2013
Parking functions and hyperplane arrangements, Mathcamp 2012, University of Puget Sound, July 2012
Orientations, semiorders, arrangements, and parking functions, SIAM Conference on Discrete Mathematics, Halifax, June 2012
The algebraic geometry of sandpiles, University of Michigan, April 2012
Sandpiles, dominos, arrangements, and ideals, Pacific University, March 2012
An invitation to sandpiles, University of Witwatersrand, February 2012
An invitation to sandpiles, University of Cape Town, February 2012
An invitation to sandpiles, Stellenbosch University, February 2012
Orientations, semiorders, arrangements, and parking functions, UTEP Colloquium Series, November 2011
Sandpiles and Dominos, UConn Math Club, October 2011
G-semiorder arrangements and G-parking functions, MIT Combinatorics Seminar, October 2011
Sandpiles and Dominos, Mathcamp 2011, Reed College, July 2011
Orientations, semiorders, arrangements, and parking functions, Reed College Mathematics Colloquium, September 2011
Some Algebraic Geometry of the Abelian Sandpile Model, Combinatorics Seminar, University of Minnesota, March 2011
Sandpiles, domino tilings, and Chebyshev polynomials, JMM New Orleans, January 2011
Some Algebraic Geometry of the Abelian Sandpile Model, MIT Combinatorics Seminar, October 2010
Domino Tilings and Sandpiles, keynote, NW Undergraduate Mathematics Symposium, Oregon State University, April 2010
The Algebraic Geometry of the Abelian Sandpile Model, Oregon State University, April 2010
The Abelian Sandpile Model, Willamette University, April 2010
Sandpiles and Tilings, Pacific University, October 2009
Sandpiles and Tilings, University of Puget Sound, September 2009
Sandpiles and Tilings, Reed College Mathematics Colloquium, April 2009
NSF-STEM presentation at Reed College, 2009