Mentoring
I've worked as an advisor at the Duluth REU program during the summers of 2017-2022. In 2023-2024, 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.
Directed reading projects:
• Kevin Cong (Harvard, fall 2023)
• Evgeni Kayryakov (Harvard, fall 2023)
• Ilaria Seidel (Harvard, fall 2023)
• Eric Shen (Harvard, fall 2023)
• Katherine Miner (MIT, spring 2023)
Undergraduate senior theses:
• Cole Yellin (Harvard, in progress)
I mentored a high school research project through the MIT PRIMES program, resulting in the following papers:
• C. Defant, D. Dong, A. Lee, and M. Wei. Connectedness and cycle spaces of friends-and-strangers graphs. To appear in Discuss. Math. Graph. Theory.
• A. Lee. Connectedness in friends-and-strangers graphs of spiders and complements. arXiv:2210.04768. Under review for publication.
I've coauthored numerous papers with undergraduates (marked in my cv).
Below are papers that resulted from Duluth REU projects that I proposed and mentored while working as an advisor in 2017-2022. The full program bibliography for the Duluth REU (including projects I supervised in 2023-2024) can be found here.
• Y. Choi and Y. Choi. Highly sorted permutations with respect to a 312-avoiding stack. Enumer. Combin. Appl., 3 (2023).
• A. Milojević. Connectivity of old and new models of friends-and-strangers graphs. Adv. Appl. Math., 155 (2024).
• Y. Choi and N. Sun. The Image of the pop operator on various lattices. Adv. Appl. Math., 154 (2024).
• A. Li. Dynamics of pop-tsack torsing. arXiv:2209.11548. Under review for publication.
• C. Defant and J. Lin. Rowmotion on m-Tamari and biCambrian lattices. Comb. Theory, 4 (2024).
• E. Hodges. On promotion and quasi-tangled labelings of posets. Ann. Comb., 28 (2024), 529-554.
• L. Hong. The pop-stack-sorting operator on Tamari lattices. Adv. Appl. Math. 139 (2022).
• R. Jeong. On structural aspects of friends-and-strangers graphs. arXiv:2203.10337. Under review for publication.
• R. Jeong. Diameters of components of friends-and-strangers graphs are not polynomially bounded. arXiv:2201.00665. Under review for publication.
• K. Bangachev. On the asymmetric generalizations of two extremal questions on friends-and-strangers graphs. European J. Combin., 104 (2022).
• I. Axelrod-Freed. 312-avoiding reduced valid hook configurations and duck words. Enumer. Combin. Appl., 1 (2021).
• C. Defant and K. Zheng. Stack-sorting with consecutive-pattern-avoiding stacks. Adv. Appl. Math., 128 (2021).
• M. Singhal. Unimodality of a refinement of Lassalle's sequence. Discrete Math., 346 (2023).
• K. Berlow. Restricted stacks as functions. Discrete Math., 344 (2021).
• C. Defant, N. Kravitz, and A. Sah. Supertrees. Electron. J. Combin., 27 (2020).
• H. Vemuri. Domination in direct products of complete graphs. Discrete Appl. Math., 285 (2020), 473--482.
• M. Sankar. Further bijections to pattern-avoiding valid hook configurations. Adv. Appl. Math., 125 (2021).
• S. Garg. Antipowers in uniform morphic words and the Fibonacci word. Discrete Math. Theor. Comput. Sci., 23 (2021).
• H. Mularczyk. Lattice paths and pattern-avoiding uniquely sorted permutations. Discrete Math. Theor. Comput. Sci., 22 (2021).
• C. Defant and N. Kravitz. Stack-sorting for words. Australas. J. Combin., 77 (2020), 51--68.
• M. Gaetz. Anti-power j-fixes of the Thue--Morse word. Discrete Math. Theor. Comput. Sci., 23 (2021).
• A. Burcroff. Domination parameters of the unitary Cayley graph of Z/nZ. Discuss. Math. Graph Theory, 43 (2023), 95--114.
• A. Burcroff. (k,λ)-anti-powers and other patterns in words. Electron. J. Combin., 25 (2018).
• N. Achenjang and A. Berger. On gaps in the closures of images of divisor functions. Int. J. Number Theory, 15 (2019), 1023--1036.
• C. Defant and S. Iyer. Domination and upper domination of direct product graphs. Discrete Math., 341 (2018), 2742--2752.
• N. Zubrilina. On the number of connected components of ranges of divisor functions. arXiv:1711.02871.