Publications
- 2025Cycle systems, coparking functions, and h-vectors of matroids, with Scott Corry, Anton Dochtermann, Solis McClain, and Lixing Yi
- 2022Simplicial Dollar Game, with Jesse Kim. Electronic Journal of Combinatorics
- 2021Counting weighted maximal chains in the circular Bruhat order, with Gopal Goel and Olivia McGough. To appear in Journal of Combinatorial Theory, Series A
- 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
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2017
G-parking functions and tree inversions, with Qiaoyu Yang and Kuai Yu. Combinatorica (arXiv)
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2016
Bigraphical arrangements, with Sam Hopkins. Transactions of the AMS
- 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.
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