David Perkinson

Professor of Mathematics
Department of Mathematics, Reed College
3203 SE Woodstock Blvd., Portland OR 97202
davidp (at) reed.edu | tel: 503-517-7417 | office: L388

CV

• 2022

Publications

• Simplicial Dollar Game, with Jesse Kim, 2022. Electronic Journal of Combinatorics, 2022.
• Counting weighted maximal chains in the circular Bruhat order, with Gopal Goel and Olivia McGough, 2021. To appear in Journal of Combinatorial Theory, Series A.
• Enumerating linear systems on graphs, with Sarah Brauner and Forrest Glebe. Mathematische Zeitschrift, 2020.
• Critical groups of iterated cones, with Gopal Goel. Linear Algebra and its Applications, 2019.
• Divisors and Sandpiles, with Scott Corry. AMS texbook, 2018.
• G-parking functions and tree inversions, with Qiaoyu Yang and Kuai Yu. Combinatorica, 2017 (arXiv version).
  • A related paper: Parking functions and tree inversions revisited, by Petar Gaydarov and Sam Hopkins, Advances in Applied Mathematics, 2016.
• Bigraphical arrangements, with Sam Hopkins. Transactions of the AMS, 2016.
  • A related paper: Multigraph Hyperplane Arrangements and Parking Functions, by Mikhail Mazin. Preprint, 2014.
• Sandpiles and Dominos, with Laura Florescu, Daniela Morar, Nick Salter, and Tianyuan Xu. Electronic Journal of Combinatorics, 2015.
• Sandpiles, spanning trees, and plane duality, with Melody Chan, Darren Glass, Matthew Macauley, Caryn Werner, and Qiaoyu Yang. SIAM Journal on Discrete Mathematics (SIDMA), 2015.
• Primer for the algebraic geometry of sandpiles, with Jacob Perlman and John Wilmes. Tropical and Non-Archimedean Geometry, Contemp. Math., 605, Amer. Math. Soc., Providence, RI, 2013
• Orientations, semiorders, arrangements, and parking functions, with Sam Hopkins. The Electronic Journal of Combinatorics, Volume 19(4), 2012.
• A Note on the Critical Group of a Line Graph, with Nick Salter and Tianyuan Xu, The Electronic Journal of Combinatorics, Volume 18(1), 2011.
• Frobenius polytopes, with John Collins, 2011.
• Permutation Polytopes and Indecomposable Elements in Permutation Groups, with R. Guralnick, Journal of Combinatorial Theory, Series A, 113, (2006), no. 7.
• Some facets of the polytope of even permutation matrices, with Jeffrey Hood, Linear Algebra and its Applications, 381 (2004).
• Eight Lectures on Monomial Ideals, with Ezra Miller, Queens Papers in Pure and Applied Mathematics, no. 120, Queen's Univ., 2001.
• Inflections of toric varieties, Michigan Math. J. , 48, 2000.
• Principal parts of line bundles on toric varieties, Compositio Mathematica 104, 1996.
• Curves in Grassmannians, Transactions of the AMS September, 1995.

Book

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

Lecture Notes

• Differential Calculus of Several Variables
• Real Analysis

Software

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

• sandpiles
• hyperplane arrangements

Presentations

• 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 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, special session on Algebro-Geometric Methods in Graph Theory at the AMS Western Sectional Meeting, Las Vegas, NV, April 2015.
• Sandpiles and Dominos, Claremont Colleges Mathematics Colloquia, Claremont, CA, February 18, 2015.
• Tree inversions and parking functions, University of Idaho, Moscow, October 23, 2014.
• Tree inversions and parking functions, special session on Computational Aspects of Algebra, Geometry and Combinatorics at MathFest, August 8, 2014.
• Project NExT panelist, Keeping Your Research Alive, Willamette University, April 13, 2013.
• Sandpiles and Dominos, McDougal Lecture in Mathematics, Lawrence University, May 2014.
• Bigraphical arrangements. PEAKS 2013, Workshop on Perspectives and Emerging Topics in Algebra and Combinatorics, Haus Bergkranz, Austria, March 22, 2013.
• The mathematics of juggling: theory and applications, African Institute for Mathematical Sciences, Cameroon, January 15, 2014.
• Invited speaker in the special session on applied combinatorics at the Mathematical Congress of the Americas, Guanajuato, Mexico, August 5–9, 2013.
• Parking functions and hyperplane arrangements . Mathcamp 2012, University of Puget Sound, July 19, 2012.
• Orientations, semiorders, arrangements, and parking functions. SIAM Conference on Discrete Mathematics, Halifax, Nova Scotia, June 19, 2012.
• The algebraic geometry of sandpiles. University of Michigan, April 6, 2012.
• Sandpiles, dominos, arrangements, and ideals. Pacific University, March 20, 2012.
• An invitation to sandpiles. University of Witwatersrand, February 14, 2012.
• An invitation to sandpiles. University of Cape Town, February 8, 2012.
• An invitation to sandpiles. Stellenbosch University, February 3, 2012.
• Orientations, semiorders, arrangements, and parking functions. UTEP Colloquium Series, November 18, 2011.
• Sandpiles and Dominos. UConn Math Club, University of Connecticut, October 30, 2011.
• G-semiorder arrangements and G-parking functions. MIT Combinatorics Seminar, October 7, 2011.
• Sandpiles and Dominos. Mathcamp 2011, Reed College, July 6, 2011.
• Orientations, semiorders, arrangements, and parking functions. Reed College Mathematics Colloquium, September 8, 2011.
• Some Algebraic Geometry of the Abelian Sandpile Model, Combinatorics Seminar at the University of Minnesota March 25, 2011.
• Sandpiles, domino tilings, and Chebyshev polynomials, Invited Paper Session on Laplacian Growth: Visual Mathematics at the Joint Mathematics Meeting, New Orleans, January 6, 2011.
• Some Algebraic Geometry of the Abelian Sandpile Model, MIT Combinatorics Seminar, Massachusetts Institute of Technology, October 20, 2010.
• Domino Tilings and Sandpiles invited keynote address for the North- west Undergraduate Mathematics Symposium at Oregon State University on April 24, 2010.
• The Algebraic Geometry of the Abelian Sandpile Model, Mathematics colloquium at Oregon State University on April 23, 2010.
• “The Abelian Sandpile Model, colloquium lecture at Willamette Uni- versity, April 1, 2010.
• Sandpiles and Tilings, colloquium lecture at Pacific University, October 5, 2009.
• Sandpiles and Tilings, colloquium lecture at University of Puget Sound Mathematics and Computer Science Department Seminar Series, September 14, 2009.
• Sandpiles and Tilings, Reed College Mathematics Colloquium, April 2, 2009.
• NFS-STEM presentation at Reed College, 2009.