Research

Matroid theory generalizes both graph theory as well as the combinatorial aspects of linear dependence in matrices. I am interested in the development of techniques to aid in characterizing the structure of highly connected matroids representable over a fixed finite field. I have used computational tools such as the SageMath software system to assist in some of my research.

My dissertation, Templates for Representable Matroids, was completed in 2018 in partial fulfillment of the requirements for my PhD at Louisiana State University. I was awarded the 2017 Pasquale Porcelli Graduate Student Research Excellence Award from the LSU Department of Mathematics.

My papers are listed below. Some are preprints or are still in preparation.

Rutger Campbell, Kevin Grace, James Oxley, and Geoff Whittle. On Density-Critical Matroids. Submitted. (arXiv)

Ben Clark, Kevin Grace, James Oxley, and Stefan H.M. van Zwam. On the Highly Connected Dyadic, Near-Regular, and Sixth-Root-of-Unity Matroids. Submitted. (arXiv)

Kevin Grace. The Templates for Some Classes of Quaternary Matroids. Submitted. (arXiv)

Nick Brettell, Rutger Campbell, Deborah Chun, Kevin Grace, and Geoff Whittle. On a Generalization of Spikes. SIAM Journal on Discrete Mathematics 33 (2019), 358-372. (arXiv, journal)

Kevin Grace and Stefan H.M. van Zwam. The Highly Connected Even-Cycle and Even-Cut Matroids. SIAM Journal on Discrete Mathematics 33 (2019), 26-67. (arXiv, journal)

Kevin Grace and Stefan H.M. van Zwam. On Perturbations of Highly Connected Dyadic Matroids. Annals of Combinatorics 22 (2018), 513-542. (arXiv, journal)

Kevin Grace and Stefan H.M. van Zwam. Templates for Binary Matroids. SIAM Journal on Discrete Mathematics 31 (2017), 254-282. (arXiv, journal)

© 2017 Kevin Grace
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