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 Potato | Combinatorics Seminar, Dartmouth College | September 2018 |

Lewis Carroll and the Red Hot Potato | Summer Combo, St. Michael's College | July 2018 |

Lewis Carroll and the Red Hot Potato | Middlebury College | March 2018 |

The Matrix Tree Theorem and the Red Hot Potato Algorithm | Hamilton College | April 2017 |

Relation between the Jones and Q Polynomial Knot Invariants | Middlebury Student Symposium, Middlebury College | April 2014 |

Stick number of knots in the hexagonal lattice | Women in Mathematics in New England (WIMIN), Smith College | September 2013 |

Graduate Student Seminar | |

The Matrix Tree Theorem and the Red Hot Potato | October 2018 |

A Fine Rediscovery | September 2017 |

Network Clustering! | February 2016 |

Domino Tilings of the Aztec Diamond | October 2015 |

**Posters**

Dodgson/Muir: Generalizing the Red Hot Potato | Discrete Math Days, University of Rhode Island | September 2018 |

Generalizing the Red Hot Potato | Graduate Poster Session, Dartmouth College | April 2018 |

Lewis Carroll and the Red Hot Potato | Discrete Math Days, Queens College | October 2017 |

The Red Hot Potato Algorithm | Graduate Poster Session, Dartmouth College | April 2017 |

Stick numbers in the hexagonal lattice | Joint Mathematics Meetings (JMM), Baltimore, MD | January 2014 |

**Publications**

- Stick numbers in the simple hexagonal lattice, with R. Bailey, H. Chaumont, E. McMahon, J. McLoud-Mann, S. Melvin, G. Schuette,
*Involve*,**8**(2015), 503-512.

**arXiv**

- Lewis Carroll and the Red Hot Potato, arXiv: 1804.00068, (2018).

**Submitted**

- Energy Policy, Environmental Studies, and Social Equity: Investigating Linkages Between Academic Concepts from Kyoto to Paris, with A. Chapman, T. Fraser, (2018).