I've worked as an advisor at the Duluth REU program during the summers of 2017-2022. In 2023-2025, I was a co-director at the Duluth REU. I've mentored several projects based on problems that have arisen from my own research. I served as a mentor for the John Locke Gap Year Program in 2018 and Princeton's Mentoring Mobius program in 2020. I've mentored 5 directed reading projects at Harvard and MIT (Kevin Cong, Evgeni Kayryakov, Ilaria Seidel, Eric Shen, Katherine Miner).
I mentored a high school research project through the MIT PRIMES program in 2022.
• Edwin Xie. Cylindrical hitomezashi patterns. arXiv:2509.04880.
• Jacob Paltrowitz. The Ungar grames on graded posets. arXiv:2509.02959.
• Ruben Carpenter. Taming irrationality: an invariance principle for the random billiard walk. arXiv:2508.12849.
• Colin Defant and Derek Liu. Homology in combinatorial refraction billiards. Res. Math. Sci., 12 (2025).
• Grant Barkley, Colin Defant, Eliot Hodges, Noah Kravitz, and Mitchell Lee. Bender--Knuth billiards in Coxeter groups. Forum Math. Sigma, 13 (2025).
• Eric Shen. Tighter bounds on the expected absorbing time of Ungarian Markov chains. arXiv:2405.11728.
• Ilaria Seidel and Nathan Sun. Periodic points of consecutive-pattern-avoiding stack-sorting maps. To appear in Discrete Math., arXiv:2308.05868.
• Janabel Xia. Deterministic stack-sorting for set partitions. Enumer. Combin. Appl., 4 (2024). arXiv:2309.14644.
• Honglin Zhu. The connectivity of friends-and-strangers graphs on complete multipartite graphs. To appear in Ann. Comb., arXiv:2307.08121.
• Honglin Zhu. The maximum number of cycles in a triangular-grid billiards system with a given perimeter. Adv. Appl. Math., 168 (2025).
• Y. Choi and Y. Choi. Highly sorted permutations with respect to a 312-avoiding stack. Enumer. Combin. Appl., 3 (2023).
• Aleksa Milojević. Connectivity of old and new models of friends-and-strangers graphs. Adv. Appl. Math., 155 (2024).
• Yunseo Choi and Nathan Sun. The Image of the pop operator on various lattices. Adv. Appl. Math., 154 (2024).
• Anqi Li. Dynamics of pop-tsack torsing. Adv. Appl. Math., 164 (2025).
• Colin Defant and James Lin. Rowmotion on m-Tamari and biCambrian lattices. Comb. Theory, 4 (2024).
• Eliot Hodges. On promotion and quasi-tangled labelings of posets. Ann. Comb., 28 (2024), 529-554.
• Letong Hong. The pop-stack-sorting operator on Tamari lattices. Adv. Appl. Math., 139 (2022).
• Ryan Jeong. On structural aspects of friends-and-strangers graphs. arXiv:2203.10337. Under review for publication.
• Ryan Jeong. Diameters of components of friends-and-strangers graphs are not polynomially bounded. Comb. Theory., 4 (2024).
• Kiril Bangachev. On the asymmetric generalizations of two extremal questions on friends-and-strangers graphs. European J. Combin., 104 (2022).
• Ilani Axelrod-Freed. 312-avoiding reduced valid hook configurations and duck words. Enumer. Combin. Appl., 1 (2021).
• Colin Defant and Kai Zheng. Stack-sorting with consecutive-pattern-avoiding stacks. Adv. Appl. Math., 128 (2021).
• Mihir Singhal. Unimodality of a refinement of Lassalle's sequence. Discrete Math., 346 (2023).
• Katalin Berlow. Restricted stacks as functions. Discrete Math., 344 (2021).
• Colin Defant, Noah Kravitz, and Ashwin Sah. Supertrees. Electron. J. Combin., 27 (2020).
• Harish Vemuri. Domination in direct products of complete graphs. Discrete Appl. Math., 285 (2020), 473--482.
• Maya Sankar. Further bijections to pattern-avoiding valid hook configurations. Adv. Appl. Math., 125 (2021).
• Swapnil Garg. Antipowers in uniform morphic words and the Fibonacci word. Discrete Math. Theor. Comput. Sci., 23 (2021).
• Hanna Mularczyk. Lattice paths and pattern-avoiding uniquely sorted permutations. Discrete Math. Theor. Comput. Sci., 22 (2021).
• Colin Defant and Noah Kravitz. Stack-sorting for words. Australas. J. Combin., 77 (2020), 51--68.
• Marisa Gaetz. Anti-power j-fixes of the Thue--Morse word. Discrete Math. Theor. Comput. Sci., 23 (2021).
• Amanda Burcroff. Domination parameters of the unitary Cayley graph of Z/nZ. Discuss. Math. Graph Theory, 43 (2023), 95--114.
• Amanda Burcroff. (k,λ)-anti-powers and other patterns in words. Electron. J. Combin., 25 (2018).
• Niven Achenjang and Aaron Berger. On gaps in the closures of images of divisor functions. Int. J. Number Theory, 15 (2019), 1023--1036.
• Colin Defant and Sumun Iyer. Domination and upper domination of direct product graphs. Discrete Math., 341 (2018), 2742--2752.
• Nina Zubrilina. On the number of connected components of ranges of divisor functions. arXiv:1711.02871.