Research Advisor: Dr. Yulan Qing, University of Tennessee at Knoxville.
Current Research:
My interests lie in Geometric Group Theory, specifically mapping class groups and curve graphs of infinite type surfaces. My current projects are joint with Dr. Yulan Qing and Andreas Thompson. We are researching the non-peripheral curve graph of infinite type surfaces with CB-generated mapping class groups, with the goal of showing one endedness and hyperbolicity.
Past Research:
My past research has been in non-Euclidean geometry, particularly taxicab/manhattan geometry, and graph theory, particularly hypergraph theory. These projects continue to shape my current work. The project that sparked my love of research and geometry was translating the shortest polyhedron problem into taxicab geometry. With my colleagues Sam Gruber and William Fulford, we created an anologue to Melzack's conjecture. This is a conjecture I hope to prove within the lifetime of my mathematical career. A love of Modern Algebra and Topology pointed me in the direction of Geometric Group Theory.
"An Analysis of Melzack's Conjecture In Taxicab Space" Joint with Sam Gruber and William Fulford, published in the International Journal of Geometry, 2021.
"On Tight 9-cycle Decompositions of Complete 3-uniform Hypergraphs" Joint with Bunge, et. al. Published in the Australasian Journal of Combinatorics in 2021.
“An Analysis of Melzak’s Conjecture in Taxicab Space.” 100th Meeting of the Southeastern Section of the Mathematical Association of America, 13 March 2021. Contributed Paper.
“On Tight 9-Cycle Decompositions of 3-Uniform Hypergraphs.” 100th Meeting of the Southeastern Section of the Mathematical Association of America, 6 March 2021. Contributed Paper.