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

Students

Each Reed College senior writes a senior thesis. The thesis is a year-long project culminating in a written document and an oral defense in front of a group of faculty drawn from across disciplines in the College.

Senior theses I have advised:

• The CW Decomposition of the Grassmannian Manifold, Anna Luce, 2022
• Kasteleyn’s Tiling Theorem Using Complex Weights, Sharon Wang, 2022
• Row motion over \(P\)-partitions, Xinling Chen, 2021
• Row motion and doppelgänger pairs, Kaitlyn Hepp, 2020
• Toppling ideals of M-matrices, Livia Xu, 2020
• 3D Sandpiles and efficient computation of the circular sandpile , Alex Grant, 2018
• Divisor theory of simplicial complexes, Jesse Kim, 2018
• A GPU approach to the Abelian sandpile model, Cameron Fish, 2017
• The stationary density and threshold density of sandpiles, Vivian Tylińska, 2017
• A knowledge-based approach to Disconnect three, Lucien Florin Feier, 2017
• M-matrices and Chip Firing, Munyo Frey-Edwards, 2016
• Split Reactive Brownian Dynamics, Qiaoyu Yang, 2016
• The Structure of the Jacobian Group of a Graph, Tessa Hoppenfeld, 2014
• Generating the Superstable Configurations of a Graph via its Acyclic Orientations, Sofia Wright, 2014
• Enumeration of Domino Tilings on the Projective Grid Graph, Wyatt Alt, 2013
• Critical Groups of Simplicial Complexes, Marcus P. Robinson, 2013
• Extending the Critical Group to Oriented Matroids and Simplicial Complexes, David Krueger, 2011
• New connections between the Abelian Sandpile Model and Domino Tilings, Laura Florescu, 2011
• Graph Partitions and Free Resolutions of Toppling Ideals, Tianyuan Xu, 2011
• Stability in chip-firing games, Tian Jiang, 2010
• The connection between dimer covers and sandpile groups, Erica Shannon, 2010
• Algebraic invariants of sandpile graphs, John Wilmes, 2010
  Related work:
  • Wilmes' Conjecture and Boundary Divisors Horia Mania
  • Minimal Free Resolutions of the G-parking Function Ideal and the Toppling Ideal Madhusudan Manjunath, Frank-Olaf Schreyer, John Wilmes
  • Monomials, Binomials, and Riemann-Roch, Madhusudan Manjunath, Bernd Sturmfels
  • Laplacian ideals, arrangements, and resolutions, Anton Dochtermann, Raman Sanyal
  • Divisors on graphs, Connected flags, and Syzygies, Fatemeh Mohammadi, Farbod Shokrieh
  • Primer for the algebraic geometry of sandpiles, David Perkinson, Jacob Perlman, John Wilmes
  • Another proof of Wilmes' conjecture, Sam Hopkins
• Permanental Ideals, Christopher Cotter, 2009 (co-advised with Irena Swanson)
• The Abelian Sandpile Model on Symmetric Graphs, Natalie Durgin, 2009 (Harvey Mudd thesis co-advised with Francis Su)
• The Tutte Polynomial and the Critical Configuration Polynomial on Acyclic Digraphs, Max Hallock, 2009
• Power Laws in the Stock Market, Dani Morar, 2009
• Sandpiles: a Bridge between Graphs and Toric Ideals, Jacob Perlman, 2009
• Riemann Roch on Directed Graphs, Jeffrey Cruse, 2008
• Circulant graphs and their spectra, Julia Lazenby, 2008. Here is an arXiv e-print based on the thesis.
• Constructing a Sandpile Machine, Rebecca Schoenberg-Jones, 2008
• The Ranks of a Tropical Matrix, Matthew Strom Borman, 2007
• Prediction and parameter estimation in the presence of missing data, Rangania Gwati, 2007
• A Category of Polytopes, Lawrence Valby, 2006
• Frameworks and Tensegrities, Ananda Floyd, 2004
• Multi-cyclic polytopes, Duncan Ramsey, 2004
• Wreath-product polytopes, Peter McMahan, 2003
• Invariant and covariant rings of finite pseudo-reflection groups, Hannah Robbins, 2002
• Cycles in the 2-ball juggling digraph, Candace Schenk, 2002
• Hilbert Functions of Finite Group Orbits: Abelian and Metacyclic Groups, Scott Corry, 2001
• Juggling State Digraphs and Multiple-Person Pattern, Ben Tombaugh, 2001
• Hilbert function of Abelian group orbits, Justin Campbell, 1999
• Convex polytopes of permutation matrices, Hana Steinkamp, 1999
• On triangulations and secondary polytopes, Ken Mitsumoto, 1997
• Combinatorics of Orbitopes, Judy Ridenour, 1996
• The Hilbert Function of the Permutahedron, Chris Fesler, 1996
• Lotsa Dots: Self-Dual Affine Monomial Varieties, John Mulliken, 1995
• Weierstrass Gap Sequences, Krishnan Ravi Shankar, 1993
• Inflections of parametrized surfaces, Oliver Gugenheim, 1993
• Watered silk: a mathematical look at Moire patterns, Tamie Veith, 1992
• Off on a tangent: an examination of concentric circles tangent to a curve, Amanda Danford, 1992
• Random thoughts in music: mathematics of randomness in music composition, Linda Young, 1991
• Goppa codes: a construction guide, Stephanie Rieser, 1991