Daniel Martin

By: Maddie Martin

I am an assistant professor at Clemson University. I study mostly number theory. My wife, Kaitlyn, and I have three daughters: Madeleine, Olive, and Charlotte. I received my PhD from the University of Colorado in 2020 under the supervision of Katherine Stange, and my postdoc was under Elena Fuchs at UC Davis. My research is supported by NSF grant #2336000. Here is my CV.

Contact:

School of Mathematical and Statistical Sciences
Clemson University
O-110 Martin Hall
220 Parkway Drive
Clemson, SC 29634

dem6@clemson.edu
(864) 656-2286

Papers:

• Markoff triples and Nielsen equivalence in SL_2(F_p). 2025.    arXiv:2510.07577    Sage code
• Lower bounds on the l-rank of ideal class groups. Submitted, 2025.    arXiv:2501.09865
• A new proof of Chen's theorem for Markoff graphs. Inventiones Mathematicae. vol. 241, pp. 623-626, 2025.    doi:10.1007/s00222-025-01346-9    arXiv:2502.15960
• Connectivity of Markoff mod-p graphs and maximal divisors (joint with Jillian Eddy, Elena Fuchs, Matthew Litman, and Nico Tripeny). Proceedings of the London Mathematical Society. vol. 130(2), e70027, 2025.    doi:10.1112/plms.70027     arXiv:2308.07579
• Fundamental polyhedra of projective elementary groups. Advances in Geometry. vol. 25(1), pp. 117-125, 2025.    doi:10.1515/advgeom-2024-0035     arXiv:2204.04790
• A geometric study of circle packings and ideal class groups. Discrete and Computational Geometry. vol. 72, pp. 181-208, 2024.    doi:10.1007/s00454-024-00638-w     arXiv:2202.10530
• Bounds on entries in Bianchi group generators. International Mathematics Research Notices. vol. 2023(11), pp. 9155-9184, 2023.    doi:10.1093/imrn/rnac092     arXiv:2110.06973
• Continued fractions over non-Euclidean imaginary quadratic rings. Journal of Number Theory. vol. 243, pp. 688-714, 2023.    doi:10.1016/j.jnt.2022.06.004     arXiv:1908.00121
• Reductions between short vector problems and simultaneous approximation. Proceedings of the Fourteenth Algorithmic Number Theory Symposium. vol. 4(1), pp. 335-351, 2020.    doi:10.2140/obs.2020.4.335     arXiv:2003.12173

Teaching:

At Clemson:

• Abstract Algebra 1 (Math 8510), Fall 2024
• Linear Algebra (Math 3110), Fall 2024
• Business Calculus (Math 1020), Fall 2023

At UC Davis:

• Number Theory (Math 115A), Fall 2022
• Modern Algebra (aka field theory, Math 150C), Spring 2022
• Differential Calculus (Math 21A), Spring 2022, Winter 2021, Fall 2020
• Modern Algebra (aka group theory, Math 150A), Winter 2022
• Discrete Math (Math 148), Winter 2022
• Real Analysis (Math 127B), Spring 2021
• Modern Algebra (aka ring theory, Math 150B), Winter 2021

At CU Boulder:

• Calculus 1 and 3 several times each