Spencer Backman's Home Page


Spencer




I am a
Postdoctoral Fellow at the Hausdorff Center for Mathematics in Bonn, Germany working with Ngoc Mai Tran.

Before coming to Bonn, I was a Postdoctoral Researcher in the Department of Computer Science at the University of Rome "La Sapienza" working with Paul Wollan

In the Spring of 2014, I received my Ph.D. in Algorithms, Combinatorics, and Optimization from the School of Mathematics at the Georgia Institute of Technology.  My PhD advisor was Matt Baker.  During 2011-2012, I spent three semesters as a Visiting Student Researcher in the Mathematics Department at the University of California Berkeley.

In the Summer of 2014, I was a Visiting Researcher at the National Institute for Mathematical Sciences in the Republic of Korea participating in the Thematic Program on Applied Algebraic Geometry

email: first name period last name at hcm.uni-bonn.de
Here is my CV.

Here is a blog post by Matt Baker about my work on Riemann-Roch theory for graph orientations.


Research:  I am interested in interactions between combinatorics, algebra, and geometry, particularly those arising in the contexts of graph theory, tropical geometry, commutative algebra, and nonarchimedean geometry.  Nearly all of my research thus far has been related, directly or indirectly, to the current development of divisor theory for graphs and tropical curves via chip-firing, which is analogous to the classical theory for algebraic curves.


Publications:

Fourientations and the Tutte Polynomial, with Sam Hopkins, accepted to Research in the Mathematical Sciences.

Partial Graph Orientations and the Tutte Polynomial
accepted to Advances in Applied Mathematics: Special Issue on the Tutte Polynomial.

Riemann-Roch Theory for Graph Orientations, to appear in Advances in Mathematics.

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:

Geometric Bijections for Regular Matroids, Zonotopes, and Ehrhart Theory, with Matthew Baker and Chi Ho Yuen.

A convolution formula for Tutte polynomials of arithmetic matroids and other combinatorial structures, with Matthias Lenz.

Fourientation Activities and the Tutte Polynomial, with Sam Hopkins and Lorenzo Traldi.

Transfinite Ford-Fulkerson on a Finite Network, with Tony Huynh. 

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.


Some miscellaneous programs in which I've participated:

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.