Exponents of Jacobians of graphs and regular matroids

H. Lheem, D. Li, C. J. Quines, and J. Zhang.
From PROMYS 2019.

PROMYS is a six-week summer camp at Boston University. Returning students of the program have the opportunity to engage in mentored research projects; ours was a topic suggested by Professor Matt Baker from Georgia Tech. Has a corresponding presentation.

Expected capture time and throttling number for cop versus gambler

J. Geneson, C. J. Quines, E. Slettnes, and S. Tsai.
From MIT PRIMES-USA 2018.

PRIMES-USA is a math research program run under MIT, where students get to work on a project provided by MIT faculty. Although the program is normally open to high school juniors studying in the United States, Espen and I were given support by MIT PRIMES to continue our work from CrowdMath. Has a presentation for the PRIMES Conference.

Variations of the cop and robber game on graphs

E. Slettnes, C. J. Quines, S. Tsai, and J. Geneson.
From CrowdMath 2017: Graph Algorithms and Applications.

CrowdMath is an open program created jointly by MIT PRIMES and the Art of Problem Solving that gives students the opportunity to collaborate on a research project. This paper is the compilation of some results discussed in several threads on the CrowdMath 2017 forum.

Bounds on metric dimension for families of planar graphs

C. J. Quines and M. Sun.

This was a project that Michael and I pursued independently of an adviser or program, which we did specifically for entry in the International Science and Engineering Fair 2017. It won Second Prize in the Mathematics category.

The conjecture on maximal planar graphs was partially resolved in the affirmative for the maximal outerplanar case by M. Claverol, et al. in Metric dimension of maximal outerplanar graphs. Has a presentation meant for a general technical audience.