M. DiPasquale, B. Gillespie, C. Peterson. "Algebra and combinatorics of uniform random arc arrangements." In preparation.

M. DiPasquale, B. Gillespie, C. Peterson. "Ehrhart Theory of Numerical Semigroup Structures." In preparation.

G. Averkov, A. Chavez, J. De Loera, B. Gillespie. "The Lattice of Cycles of an Undirected Graph." *Linear Algebra and its Applications*, 611(3), 2020.

B. Gillespie. "Convexity in Ordered Matroids and the Generalized External Order." *The Electronic Journal of Combinatorics*, 27(3):P3.41, 2020.

B. Gillespie. "The Generalized External Order, and Applications to Zonotopal Algebra." PhD Thesis, University of California, Berkeley. 2018.

B. Gillespie. "Extending Redheffer's Matrix to Arbitrary Arithmetic Functions." 2011. (PDF)

B. Gillespie. "On Randomness of Subsets of Z_N, as Described by Uniformity of Fourier Coefficients." 2010. (PDF)

B. Gillespie. "Discrete Convexity and the Active Matroid Orders." Algebra and Algebraic Geometry, I, 2020 Joint Mathematics Meetings. Denver, CO. 17 Jan. 2020.

B. Gillespie. "Convexity in Ordered Matroids and the Generalized External Order." Topology Seminar, Colorado State University. Fort Collins, CO. 10 Dec. 2019.

B. Gillespie. "Circuit Lattices of Graphs and Matroids." CACAO Seminar, University of California, Davis. Davis, CA. 5 Mar. 2019.

B. Gillespie. "Matroids, Antimatroids, and the External Order." Algebra and Discrete Mathematics Seminar, University of California, Davis. Davis, CA. 20 Nov. 2017.

B. Gillespie. "Polymatroids, Zonotopes, and Images of Rational Maps of Projective Spaces." Special Seminar, University of California, Berkeley. Berkeley, CA. 30 Sep. 2015.

B. Gillespie. "Zonotopal Algebra." Graduate Student Combinatorics Conference, University of Kentucky. Lexington, KY. 29 Mar. 2015.

B. Gillespie. "Planar Bond Percolation: An Example of a Nontrivial Phase Transition." Many Cheerful Facts, University of California, Berkeley. Berkeley, CA. 11 Apr. 2012.

B. Gillespie and T. London. "Semi-dispersing Billiards and Infinite Topological Entropy." Young Mathematicians Conference, Ohio State University. Columbus, OH. 17 Aug. 2007.