Knot Colorability and Maximum Knot Determinants

I attended the 2021 Summer Undergraduate Research Institute in Experimental Mathematics (SURIEM) at Michigan State University. While I was there, I did research on the colorability of knots under the mentorship of Dr. Matthew Hedden and Dr. Teena Gerhardt. My final report is available here. I have presented our work at the following conferences:

  • 2021 Summer Undergraduate Michigan Mathematics Research Conference [slides]
  • 2022 Joint Mathematics Meeting – Pi Mu Epsilon Poster Session [poster]
  • 2022 Nebraska Conference for Undergraduate Women in Mathematics [slides]

Through our research, we were able to find a lower bound for the maximum determinants of knots and links on squares grids. We also establish a connection between determinants of knots and links on grid diagrams and the Hadamard matrices.

Graph Neural Networks

Through the Helen Fellowship and Robot Autonomy and Interactive Learning (RAIL) Laboratory at Georgia Tech, I have conducted research on graph neural networks and their applications to spatio-temporal object tracking. This work has been done under the mentorship of professor Dr. Sonia Chernova and graduate student Maithili Patel.