Spencer Backman's Home Page

I am an Assistant 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.

In preparation: • Higher Categorical Associahedra, with Nathaniel Bottman and Daria Poliakova • Skeletal Parking Functions and Dyck Paths, with Cole Charbonneau, Patrick Mullins, Mazie O'Connor, and Greg Warrington Publications: • Matroid Chern-Schwartz-MacPherson Cycles and Tutte Activities, with Ahmed Ashraf, Proceeding of the American Mathematical Society, 151 (2023), 2303-2309. • Simplicial Generation of Chow Rings of Matroids, with Christopher Eur and Connor Simpson, Journal of the European Mathematical Society (2023). • 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, Page 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: • A Regular Unimodular Triangulation of the Matroid Base Polytope, with Gaku Liu. • Fan Valuations and Spherical Intrinsic Volumes, with Sebastian Manecke and Raman Sanyal. • Topological Bijections for Oriented Matroids, with Francisco Santos and Chi Ho. • Cone Angles, Gram's Relation, and Flag-Angles, with Sebastian Manecke and Raman Sanyal • 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, for the CRC Handbook on the Tutte Polynomial and Related Topics, (to appear). Blog Posts: Here are some blog posts by Matt Baker about my work on Riemann-Roch theory for graph orientations, and my work with Baker and Yuen on The circuit-cociruit reversal system and torsor structures on spanning trees.

Some miscellaneous programs in which I've participated: Thematics Program on Applied Algebraic Geometry at the National Institute of Mathematical Sciences in South Korea Budapest Semesters in Mathematics Math in Moscow - Here are some photos of my class and me. Emory Tibet Science Initiative - Here's a photo of me with my monk students at Sarah College, Dharamsala after teaching them about Cantor's theory of infinity.