Spencer Backman's Home Page

I am an Associate Professor in the Department of Mathematics and Statistics at the University of Vermont email: firstnamedotlastnameatuvmdotedu Here is my CV.

Research:  I am interested in interactions between combinatorics, algebra, and geometry, particularly those arising in the context of matroid theory, graph theory, polytope theory, tropical geometry, commutative algebra, and nonarchimedean geometry.

Publications: • Extension-lifting Bijections for Oriented Matroids, with Francisco Santos and Chi Ho Yuen, Discrete and Computational Geometry (to appear). • Cone Angles, Gram’s Relation, and Flag-Angles, with Sebastian Manecke and Raman Sanyal, Algebraic Combinatorics (to appear). • Skeletal Generalizations of Parking Functions, Dyck Paths, and Chip-firing Games, with Cole Charbonneau, Nicholas A. Loehr, Patrick Mullins, Mazie O'Connor, and Gregory S. Warrington, Combinatorial Theory, 5(4). • A Regular Unimodular Triangulation of the Matroid Base Polytope, with Gaku Liu, Duke Mathematical Journal 174(14): 3047-3061. • Simplicial Generation of Chow Rings of Matroids, with Christopher Eur and Connor Simpson, Journal of the European Mathematical Society, 26, 4491–4535 (2024). • Fan Valuations and Spherical Intrinsic Volumes, with Sebastian Manecke and Raman Sanyal, Annals of Combinatorics, (2024): 1-18. • Matroid Chern-Schwartz-MacPherson Cycles and Tutte Activities, with Ahmed Ashraf, Proceedings of the American Mathematical Society, 151 (2023), 2303-2309. • A Convolution Formula for Tutte Polynomials of Arithmetic Matroids and Other Combinatorial Structures, with Matthias Lenz, Séminaire Lotharingien de Combinatoire, [B78c] 2021, 17pp.   • Geometric Bijections for Regular Matroids, Zonotopes, and Ehrhart Theory, with Matthew Baker and Chi Ho Yuen, Forum of Mathematics, Sigma, Volume 7, 2019, e45. • Transfinite Ford-Fulkerson on a Finite Network, with Tony Huynh, Computability, vol. Pre-press, No. Pre-press, pp. 1-7, 2018. • Fourientation Activities and the Tutte Polynomial, with Sam Hopkins and Lorenzo Traldi, European Journal of Combinatorics, Volume 67, January 2018, Pages 40-60. • Fourientations and the Tutte Polynomial, with Sam Hopkins, Research in the Mathematical Sciences, 2017 4:18. • Partial Graph Orientations and the Tutte Polynomial, Advances in Applied Mathematics, Special Issue for the Tutte Polynomial, Volume 94, March 2018, Pages 103-119. • Riemann-Roch Theory for Graph Orientations, Advances in Mathematics, Volume 309, March 2017, Pages 655-691. • Explicit Deformation of Lattice Ideals via Chip Firing Games on Directed Graphs, with Madhusudan Manjunath, Journal of Algebraic Combinatorics, Volume 42, Issue 4, December 2015, Pages 1097-1110. • Infinite Reduction of Divisors on Metric Graphs, European Journal of Combinatorics, Volume 35, January 2014, Pages 67-74. • Sum-product inequalities with perturbation, with Ernie Croot, Mariah Hamel, and Derrick Hart, INTEGERS Volume 11A (2011) Proceedings of the Integers Conference 2009 in Honor of the Birthdays of Melvyn Nathanson and Carl Pomerance.

Preprints: • Quantized Rational Chip-Firing, with Nicholas A. Loehr and Gregory S. Warrington. • Line Shellings of Geometric Lattices, with Galen Dorpalen-Barry, Anastasia Nathanson, Ethan Partida, and Noah Prime. • Ford Spheres in the Clifford-Bianchi Setting, with Taylor Dupuy, Anton Hilado, and Veronika Potter. • Higher-Categorical Associahedra, with Nathaniel Bottman and Daria Poliakova. • Convex Geometry of Building Sets, with Rick Danner. • A Bijection Between the Recurrent Configurations of a Hereditary Chip-Firing Model and Spanning Trees • Chip-Firing and Riemann-Roch Theory for Directed Graphs, with Arash Asadi. Book Chapter: • Tutte Activities, in the Handbook of the Tutte Polynomial and Related Topics, CRC Press, 2022. Photo with monastic students at Sarah College, Dharamsala (Emory–Tibet Science Initiative, 2013).