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Scholarship

My research interests fall under the umbrella of knot theory, a branch of topology. At Bryn Mawr College, my dissertation work under the advisement of Dr. Lisa Traynor specifically focused on contact topology and symplectic geometry. Legendrian knots, which have some additional geometric structure, are important objects of study in contact topology. Since graduate school, my research interests have focused on properties of both smooth and Legendrian knots. I am particularly interested in mosaic representations of both Legendrian and smooth knots. The visual and tactile nature of knot mosaics lends itself to undergraduate involvement, and has been the topic for four projects that I have collaborated on with students both at my home institution and at the Moravian REU. In addition, I am interested in recreational math topics, particularly the intersection between mathematics and art.

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Publications

  •  Constructions of and bounds on the toric mosaic number, joint with Kendall Heiney*, Margaret Kipe*, Kaelyn Pontes*, and Luc Ta*, (2024). (In Preparation)​

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  • Bounds on mosaic number of Legendrian knot mosaics, joint with Margaret Kipe*, Leif Schaumann*, Luc Ta*, and Wing Hong Tony Wong, (2024). (Submitted) arXiv:2410.08064

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  • Mathemalchemy: an invitation to play, joint with Rochy Flint, Faye Goldman, Li-Mei Lim, and Daina Taimina, MAA Focus Magazine, Vol. 44. No. 5. October 2024.​

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  • Integer sequences ``AA374939", ``AA374942", ``AA374943", ``AA374944", ``AA374945", ``AA374946", and ``AA374947" related to Legendrian knot mosaics in the On-Line Encyclopedia of Integer Sequences, joint with Margaret Kipe, Leif Schaumann, Luc Ta, and Wing Hong Tony Wong. OEIS Foundation Inc. (2024), https://oeis.org/A374939.

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  • Cubic knot mosaics, joint with Trevor Meintel*, and Aaron Shabon*, Involve (2024). (Accepted)​

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  • Geography of Legendrian Knot Mosaics, , joint with Abhinav Pandey*, Journal of Knot Theory and Its Ramifications (2022), Vol. 31. No. 01.​

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  • Exploring and Extending the Impossible Card Location Trick, joint with Giovanni DiCicco*, Aditya Kommoju*, and Dhanush Rajesh*, The College Mathematics Journal (2021), 52:5, 356-363, DOI: 10.1080/07468342.2021.1967696

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  • Constructions of Lagrangian cobordisms, joint with Sarah Blackwell, Noemie Legout, Cailtin Leverson, Maylis Limouzineau, Ziva Myer, Yu Pan, Lara Simone Suárez, and Lisa Traynor. In: Research Directions in Symplectic and Contact Geometry and Topology (2020), Association for Women in Mathematics Series, vol 27. Springer, Cham.​

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  • Immersed Lagrangian Fillings of Legendrian Submanifolds via Generating Families. PhD Diss., Bryn Mawr College, 2018.

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*Indicates student co-author

Additional Links

Mathemalchemy: Conceived in early Fall 2019, as the brainchild of mathematician Ingrid Daubechies and fiber artist Dominique Ehrmann, the Mathemalchemy project became in 2020 an exciting collaborative enterprise, driven by the energy and enthusiasm of twenty-four mathematical artists and artistic mathematicians

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