Academic Title

Associate Professor, Mathematics

Research Interests
  • Knot Theory
  • Recreational Mathematics
  • Spatial Graph Theory
Research Summary

My current research involves studying different ways certain types of graphs can be embedded in three-dimensional space, and understanding the collection of knotted links and cycles in these spatial embeddings. This work is motivated by my interest in representations of graphs that are minimally entangled. In addition to my research in knots and spatial graphs, I am also interested in recreational mathematics, especially the mathematics of games. I have worked on projects involving cribbage, Candy Crush, Carcassonne, Swish and Sagrada, and I am eager to involve undergraduates in my work!

  • Ph.D., Mathematics, Stanford University
  • M.S., Mathematics, Stanford University
  • B.A., Mathematics and English, University of Notre Dame
Recent Publications

Classification of book representations of K_6. Journal of Knot Theory and Its Ramifications. 2017;26(12):1750075. doi:10.1142/s0218216517500754.

(with belcastro, s-m.) “An Elementary Computation of the Conway Polynomial for (m,3) and (m,4) Torus Links,” Journal of Combinatorial Mathematics and Combinatorial Computing, February 2016, 96, 159-170.

“Candy Crush Combinatorics.” The College Mathematics Journal. 2015;46(4):255. doi:10.4169/college.math.j.46.4.255.

(with Politano, A.) “Knots in the Canonical Book Representation of Complete Graphs.” Involve, a Journal of Mathematics. 2013;6(1):65-81. doi:10.2140/involve.2013.6.65.