Bennet Goeckner

University of Washington

My research interests lie primarily in topological combinatorics and have connections to discrete geometry and commutative algebra. I am particularly interested in studying the interplay of various algebraic, topological, and combinatorial properties of simplicial complexes. I also study matching complexes, polytopes, and universal partial words.

These interactive graphics of a combinatorial cube with perpendicular opposing facets and a pentagon with its type cone illustrate some phenomena studied in my recent preprint "Minkowski summands of cubes."

I especially enjoy doing research with undergraduates, and my projects have aspects that are well-suited for student involvement. See my student research page for more information on this in particular.

Research articles

The symbol * indicates an undergraduate coauthor.

A characterization of two-dimensional Buchsbaum matching complexes
with Fran Herr*, Legrand Jones II*, and Rowan Rowlands.
Preprint.
arXiv
Minkowski summands of cubes
with Federico Castillo, Joseph Doolittle, Michael Ross, and Li Ying.
Bulletin of the London Mathematical Society, to appear.
arXiv
Partition and Cohen–Macaulay extenders
with Joseph Doolittle and Alex Lazar.
European Journal of Combinatorics, to appear.
arXiv
Resolving Stanley's conjecture on k-fold acyclic complexes
with Joseph Doolittle.
Combinatorial Theory, to appear.
arXiv
Sage code
Lattice polytopes from Schur and symmetric Grothendieck polynomials
with Margaret Bayer, Su Ji Hong, Tyrrell McAllister, McCabe Olsen, Casey Pinckney, Julianne Vega, and Martha Yip.
Electronic Journal of Combinatorics, 28 (2021), no. 2, 36pp.
arXiv
Journal
Manifold matching complexes
with Margaret Bayer and Marija Jelić Milutinović.
Mathematika 66(4), 973–1002. (2020).
arXiv
Journal
Higher nerves of simplicial complexes
with Hailong Dao, Joseph Doolittle, Ken Duna, Brent Holmes, and Justin Lyle.
Algebraic Combinatorics, Volume 2 (2019) no. 5, p. 803–813.
arXiv
Journal
Universal partial words over non-binary alphabets
with Corbin Groothuis, Cyrus Hettle, Brian Kell, Pamela Kirkpatrick, Rachel Kirsch, and Ryan Solava.
Theoretical Computer Science 713, 56–65. (2018).
arXiv
Journal
A non-partitionable Cohen–Macaulay simplicial complex
with Art Duval, Caroline Klivans, and Jeremy Martin.
Advances in Mathematics 299, 381–395. (2016).
arXiv
Journal

Selected talk slides

See my CV for a complete list of the conference, seminar, and colloquium talks I've given.

Partition extenders, skeleta of simplices, and Simon's conjecture
ECM Applied Combinatorial Topology Minisymposium
Slides
Type cones and products of simplices
AMS Special Session on Algebraic, Geometric and Topological Combinatorics
Slides
Cube
Type Cone
Manifold matching complexes
AMS Special Session on Research from the Rocky Mountain-Great Plains Graduate Research Workshop in Combinatorics
Slides
Resolving Stanley's conjecture on k-fold acyclic complexes
AMS Special Session on Geometric and Topological Combinatorics
Slides