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Presenting at the Innovative Pedagogy in Geometry and Topology Workshop at Oberlin College in July 2023.
Mathematical Interests:
Mathematical Interests:
Some of my research work is at the intersection of hyperbolic geometry and low-dimensional topology. I am interested in geometric and topological invariants of hyperbolic 3-manifolds, especially hyperbolic knot and link complements. My thesis and early research work focused on analyzing symmetries, hidden symmetries, and commensurability classes of these manifolds, along with connections to their length spectra. My thesis advisor was Dave Futer. My more recent work in geometric topology has involved a series of projects with Rollie Trapp (CSUSB) focused on exploiting the hyperbolic structures of fully augmented link complements to analyze the topology of these links and their respective complements .
I have also worked with undergraduate students on a variety of mathematical research projects, several of which have been in combinatorial topology. Several of these projects involved analyzing embeddings of Cartesian products of graphs on surfaces.
Finally, I have started working on projects at the intersection of historical cryptology, mathematics, and data analysis. I am interested in developing and improving algorithms and quantitative tools to assist with the cryptanalysis of classical ciphers, such as the Vigenere cipher, the Playfair cipher, and the Hill Cipher.
A copy of my CV can be found here.
The * symbol denotes an undergraduate student research collaborator.
Preprints and Works in Progress:
Projective Planar Cartesian Products of Graphs. (Submitted)
Joint with N. Abell* and E. McDermott*
Joint with E. Badgett*
Joint with R. Trapp
Publications:
Using Integer Programming to Solve Games, Puzzles, and Ciphers, accepted in Foundations for Undergraduate Research in Mathematics (Springer).
Joint with L. Bouzarth, J. Harris, and K. Hutson
Symmetry Groups of Hyperbolic Links and Their Complements, published in The Journal of Knot Theory and Its Ramifications 34-8 (2025), Paper 2550033, 17 pages. DOI 10.1142/S0218216525500336, arXiv: 2403.17616
Joint with R. Trapp
Flat Fully Augmented Links are Determined by Their Complements, published in Algebraic & Geometric Topology 25-8 (2025), 4839--4896. DOI 10.2140/agt.2025.25.4839.
Joint with R. Trapp
An artificial neural network approach to finding the key length of the Vigenere cipher, published in Cryptologia Vol. 49 (4), 331-347 (2025). https://doi-org.libproxy.furman.edu/10.1080/01611194.2024.2351117
Joint with Y. Yau
Joint with M. Carns*, A. Pate*, and Y. Yau, published in Cryptologiam Vol. 48 (6), 558-573 (2024). https://www.tandfonline.com/doi/full/10.1080/01611194.2023.2275583
Deciphering Secrets Throughout History: An Interdisciplinary Linguistics and Cryptology Course.
Joint with E. Kim, published in the 6th International Conference on Historical Cryptology HistoCrypt 2023.
Joint with N. Hoffman and W. Worden, published in Algebraic & Geometric Topology, 22-2 (2022), 601-656. https://msp.org/agt/2022/22-2/p03.xhtml
Joint with Fabian Salinas* (Summer 2020 Furman Advantage Summer Research Project), published in Graphs and Combinatorics, Vol. 38, 87 (2022). https://doi.org/10.1007/s00373-022-02488-w
Joint with E. Chesebro, J. DeBlois, N. Hoffman, P. Mondal, and W. Worden, published in International Mathematics Research Notices (2022). rnac018, https://doi.org/10.1093/imrn/rnac018
Joint with J. Meyer and R. Trapp, published in New York J. Math., Vol. 26 (2020), 149-183.
Published in Communications in Analysis and Geometry, Vol. 25, No. 3 (2017), 625-683.
Joint with D. Futer, published in Proceedings of the London Mathematical Society, Vol. 115, No. 2 (2017), 411-447.
Joint with W. Worden, published in Pacific Journal of Mathematics, Vol. 285, No. 2 (2016), 453-484.
Published in The Proceedings of the American Mathematical Society, Vol. 143, No. 5 (2015) 2201-2214.
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