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Picture taken from my talk at the Temple University Geometry & Topology Seminar in March 2019.
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 more recent work in geometric topology with Rollie Trapp (CSUSB) has largely focused on exploiting the hyperbolic structures of fully augmented link complements to analyze the topology of these links and their respective complements . My thesis advisor was Dave Futer.
I have also worked with undergraduate students on a variety of mathematical research projects, several of which have been in topological graph theory. Many of these projects have 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*
Symmetry Groups of Flat Fully Augmented Links and Their Complements. (In progress)
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, accepted for publication in The Journal of Knot Theory and Its Ramifications. https://www.worldscientific.com/doi/10.1142/S0218216525500336
Joint with R. Trapp
Flat Fully Augmented Links are Determined by Their Complements, accepted for publication in Algebraic & Geometric Topology.
Joint with R. Trapp
An artificial neural network approach to finding the key length of the Vigenere cipher, published in Cryptologia (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 Cryptologia (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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