Posts by Collection

Distinct Angles and Angle Chains in Three Dimensions

Published in Discrete Mathematics & Theoretical Computer Science, 2023

A three-dimensional analogue of the Erdős distinct distance problem, bounding the minimum number of distinct angles determined by point configurations in general position.

Recommended citation: Ascoli, R., Betti, L., Lehmann Duke, J., Liu, X., Milgrim, W., Miller, S. J., Palsson, E. A., Romero Acosta, F., and Velazquez Iannuzzelli, S. (2023). "Distinct angles and angle chains in three dimensions." Discrete Mathematics & Theoretical Computer Science, 25(1), Combinatorics. https://doi.org/10.46298/dmtcs.10037
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Towards the Gaussianity of Random Zeckendorf Games

Published in Combinatorial and Additive Number Theory (CANT) conference proceedings, 2023

Evidence toward Gaussian behavior in the random Zeckendorf game, building on the two-player game of Baird, Epstein, Flint, and Miller.

Recommended citation: Cheigh, J., Dantas e Moura, G. Z., Jeong, R., Lehmann Duke, J., Milgrim, W., Miller, S. J., and Ngamlamai, P. (2023). "Towards the Gaussianity of random Zeckendorf games." Combinatorial and Additive Number Theory (CANT) conference proceedings.
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An Invitation to Fibonacci Digits

Published in The Fibonacci Quarterly, 2025

A short note on the interplay between math outreach and original research, growing out of questions about Zeckendorf-style decompositions.

Recommended citation: Cheigh, J., Dantas e Moura, G. Z., Lehmann Duke, J., Mauro, A., McDonald, Z., Mello, A., Miller, K., Miller, S. J., and Velazquez Iannuzzelli, S. (2025). "An invitation to Fibonacci digits." The Fibonacci Quarterly, 63(4), 702-710.
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Topological Methods in Zero-Sum Ramsey Theory

Published in Forum of Mathematics, Sigma, 2025

Topological approach to zero-sum Ramsey theory, extending the Erdős-Ginzburg-Ziv theorem, with applications to Kneser hypergraphs.

Recommended citation: Frick, F., Lehmann Duke, J., McNamara, M., Park-Kaufmann, H., Raanes, S., Simon, S., Thornburgh, D., and Wellner, Z. (2025). "Topological methods in zero-sum Ramsey theory." Forum of Mathematics, Sigma, 13, e192. https://doi.org/10.1017/fms.2025.10125
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Ergodicity and Algebraicity of the Fast and Slow Triangle Maps

Published in Ergodic Theory and Dynamical Systems, 2026

Senior thesis proving ergodicity of the fast and slow triangle maps, later published in Ergodic Theory and Dynamical Systems.

Recommended citation: Garrity, T. and Lehmann Duke, J. (2026). "Ergodicity and algebraicity of the fast and slow triangle maps." Ergodic Theory and Dynamical Systems, 46(1), 93-127. https://doi.org/10.1017/etds.2025.10198
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The Far-Difference Game

Published: July 01, 2022

A live virtual talk on the far-difference game, given at the Twentieth International Fibonacci Conference.

Distinct Angles and Angle Chains in Three Dimensions

Published: August 01, 2022

On general position point configurations in three dimensions that minimize the number of distinct angles — joint work from the SMALL REU at Williams. See the paper.

Zeckendorf-Style Decompositions of Integers into Fibonacci Numbers

Published: August 02, 2022

The second of two talks given at YMC 2022, on Zeckendorf-style decompositions of integers into Fibonacci numbers and the associated games. See the paper.

Generalizations of the Erdős-Ginzburg-Ziv Theorem via Topology

Published: August 01, 2023

On topological approaches to zero-sum problems generalizing the Erdős-Ginzburg-Ziv theorem, arising from the Geometry and Topology in a Discrete Setting REU at Carnegie Mellon. See the paper.

Topological Methods in Zero-Sum Ramsey Theory

Published: January 03, 2024

Invited to present research in topological combinatorics at the JMM 2024 poster session. See the paper.

Ergodicity and Algebraicity of the Fast and Slow Triangle Maps (Thesis Defense)

Published: May 06, 2024

Defense of my undergraduate honors thesis in dynamical systems and multidimensional continued fraction theory, advised by Professor Thomas Garrity. Awarded Highest Honors.

The Rigidity Lemma and the Theorem of the Cube

Published: September 30, 2025

A talk in the Math 150 learning seminar on abelian varieties, covering the rigidity lemma and the theorem of the cube.

Guest Lecture on Ring Theory

Published: November 06, 2025

A two-hour guest lecture on ring theory, given as part of my role as “super” teaching assistant for Math 71 (Abstract Algebra).

Teaching experience 1

Undergraduate course, University 1, Department, 2014

This is a description of a teaching experience. You can use markdown like any other post.

Teaching experience 2

Workshop, University 1, Department, 2015

This is a description of a teaching experience. You can use markdown like any other post.