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I am a PhD candidate in mathematics at the University of Vermont, advised by Professor Puck Rombach. In December 2017, I recieved a Bachelors of Arts in Mathematics and English, also from UVM. For a year, I taught English language courses at two middle schools near Nantes, France. Now, I thoroughly enjoy my research in graph theory and my role as a graduate student instructor.

My research primarily concerns combinatorial graph theory. I am interested in other areas of combinatorics too, including extremal problems and matroid theory. Last year, I applied these skills to a project on satellite communication networks as a graduate research assistant.

CV (PDF)»

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Publications & Preprints

A lower bound on the saturation number and a strengthening for triangle-free graphs, CB, Puck Rombach; arXiv:2402.11387, 2024.

Tropical Geometry of Rado Matroids, CB, Rick Danner; arXiv:2402.04186, 2024.

Node Placement to Maximize Reliability of a Communication Network with Application to Satellite Swarms, CB, James Bagrow, Puck Rombach, and Hamid Ossareh; 2023 IEEE International Conference on Systems, Man, and Cybernetics (SMC).

Toughness of recursively partitionable graphs, CB, Brandon Du Preez, K. E. Perry, and Puck Rombach; Theory and Applications of Graphs, Vol. 10: Iss. 2, Article 4, 2023.

Path odd-covers of graphs, Steffen Borgwardt, CB, Eric Culver, Bryce Frederickson, Puck Rombach, and Youngho Yoo; arXiv:2306.06487, 2023.

Odd covers of graphs, CB, Alexander Clifton, Eric Culver, Jiaxi Nie, Jason O'Neill, Puck Rombach, and Mei Yin; J. Graph Theory, 2023.

On the last new vertex visited by a random walk in a directed graph, CB, Paul Horn, and Puck Rombach; Discrete Math. Lett., 11:96-98, 2023.

Subgraph complementation and minimum rank, CB, Christopher Purcell, Puck Rombach; Electr. J. Comb., 29(1), Feb 2022.

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Talks & Posters

List of both upcoming and past talks

Slides on the last new vertex visited by a random walk in a directed graph, for the 54th SEICCGTC

Slides on subgraph complementation and minimum rank, and a poster for the 2021 NE Combinatorics Network KLATCH

Poster on odd covers of graphs for the 2022 Discrete Math Days

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Workshops

MASI Masamu Advanced Study Institute and Workshops (virtual in 2020 and 2021, Pretoria, South Africa in 2023). I participated each time in the graph theory work group, meeting many wonderful people with many wonderful problems to work on. The 2020 and 2021 workshops lead to the paper "Toughness of recursively partitionable graphs," the idea for the paper "On the last new vertex vistited by a random walk in a directed graph" was hatched at the 2021 workshop, and a project from the 2023 workshop is underway.

GRWC Graduate Research Workshop in Combinatorics (virtual in 2021, Denver, CO in 2022). I had the pleasure of working on a number of problems suggested by my fellow graduate students and of leading working groups on odd covers of graphs with bicliques in 2021 and on odd covers with paths and cycles in 2022.

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Teaching

Math1212 Fundamentals of Calculus I (Fall 2019, 2020, 2021)

• Lesson plans: an intuitive approach to calculating Riemann sums and integration by substitution

Math1077 Exploring Modern Mathematics (Spring 2020, 2021, 2024)

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Outreach

Lessons designed to make combinatorics acccessible to a large audience.

Lights Out Can you turn off all the lights? Exercises range from simple to challenging.

Eventown and Oddtown How many (odd/even) clubs can we form if any two clubs must share an even number of people?

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Links

Youtube lectures Video lectures from Spring 2020 Math017 Applications of Finite Math.

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Awards and Honors

Nam Sang Kil Scholarship in Mathematics UVM (2023)

GTA Graduate Teaching Assistant of the Year, Lecture Instruction Category, UVM (2021)

Kenney John F. Kenney Award for excellence in mathematics, UVM (2021)

AMS American Mathematical Society Travel Grant, Joint Mathematics Meetings (Virtual 2021, San Francisco 2024)

Phi Beta Kappa Alpha of Vermont, UVM (2017)

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Contact

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