Research Interests

My research interests are in combinatorics, specifically graph theory. I am currently working with my advisor, Peter Doyle, on examining the interplay between linear algebra identities and graph theoretic identities.

I also do some work with networks. Most recently, I worked with political scientists to examine citation networks in energy policy.

In undergraduate, I also worked on knot theory, specifically finding lower bounds on stick number of knots in the hexagonal lattice.

For more information, please read my research statement.


Abstracts

Lewis Carroll and the Red Hot Potato
The Lewis Carroll identity expresses the determinant of a matrix in terms of subdeterminants obtained by deleting one row and column or a pair of rows and columns. Using the matrix tree theorem, we can convert this into an equivalent identity involving sums over pairs of forests. Unlike the Lewis Carroll Identity, the Forest Identity involves no minus signs. Using the Involution Principle, we can pull back Zeilberger's proof of the Lewis Carroll Identity to a bijective proof of the Forest Identity. This bijection is implemented by the Red Hot Potato algorithm, so called because the way edges get tossed back and forth between the two forests is reminiscent of the children's game of hot potato.

Energy Policy, Environmental Studies, and Social Equity: Investigating Linkages Between Academic Concepts from Kyoto to Paris.
with A. Chapman and T. Fraser
Just over twenty years ago, the Kyoto Protocol brought nations together to address the emergent issue of climate change. To support the development of energy policy, a number of academic fields were strengthened, particularly surrounding sustainable development and the economic, environmental and social aspects of sustainability. This research focuses on the social aspects, beginning with climate justice, through to the emergence of energy justice and the notion of a just transition. Through a bibliometric analysis of academic literature incorporating energy policy, environmental studies, and social equity across relevant academic fields over the past twenty years, strong linkages among five distinct schools of thought were identified. Some geographic stratification is occurring among these schools, notably between the US, which focuses on environmental justice and energy policy, and the EU, which tends to focus on energy justice and energy transitions. Interestingly, energy transitions scholarship appears distinct from social equity and justice related scholarship, while the issues of gender, income, class, and representation are understudied in energy policy. There is a need to better integrate disparate schools of thought in order to achieve a just transitions framework able to address inequities in energy policy outcomes in the Paris Agreement era and beyond.

Stick numbers in the simple hexagonal lattice
with R. Bailey, H. Chaumont, E. McMahon, J. McLoud-Mann, S. Melvin, G. Schuette
In the simple hexagonal lattice, bridge number is used to establish a lower bound on stick numbers of knots. This result aids in giving a new proof that the minimal stick number is 11. In addition, the authors establish upper bounds for the stick number of a composite knot. Constructions for (p,p+1)-torus knots and some 3-bridge knots are given requiring one more stick than the lower bound guarantees.


Talks

Lewis Carroll and the Red Hot PotatoCombinatorics Seminar, Dartmouth CollegeSeptember 2018
Lewis Carroll and the Red Hot PotatoSummer Combo, St. Michael's CollegeJuly 2018
Lewis Carroll and the Red Hot PotatoMiddlebury CollegeMarch 2018
The Matrix Tree Theorem and the Red Hot Potato AlgorithmHamilton CollegeApril 2017
Relation between the Jones and Q Polynomial Knot InvariantsMiddlebury Student Symposium, Middlebury CollegeApril 2014
Stick number of knots in the hexagonal latticeWomen in Mathematics in New England (WIMIN), Smith CollegeSeptember 2013

Graduate Student Seminar
The Matrix Tree Theorem and the Red Hot PotatoOctober 2018
A Fine Rediscovery September 2017
Network Clustering! February 2016
Domino Tilings of the Aztec DiamondOctober 2015


Posters

Dodgson/Muir: Generalizing the Red Hot PotatoDiscrete Math Days, University of Rhode IslandSeptember 2018
Generalizing the Red Hot PotatoGraduate Poster Session, Dartmouth CollegeApril 2018
Lewis Carroll and the Red Hot PotatoDiscrete Math Days, Queens CollegeOctober 2017
The Red Hot Potato AlgorithmGraduate Poster Session, Dartmouth CollegeApril 2017
Stick numbers in the hexagonal latticeJoint Mathematics Meetings (JMM), Baltimore, MDJanuary 2014


Publications

arXiv

Submitted