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. This year, I was awarded the 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.

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

Kevin Grace and Stefan H.M. van Zwam. A problematic family of dyadic matroids. Submitted. (arXiv)

Kevin Grace and Stefan H.M. van Zwam. The highly connected even-cycle and even-cut matroids. Submitted. (arXiv)

Kevin Grace. The templates for some classes of quaternary matroids. In preparation.

Ben Clark, Kevin Grace, James Oxley, and Stefan H.M. van Zwam. The templates for dyadic matroids. In preparation.

Nick Brettell, Rutger Campbell, Deborah Chun, Kevin Grace, and Geoff Whittle. A generalization of spikes. In preparation.

© 2017 Kevin Grace
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