Pioneer Research — Knot Theory

During the 2026 Pioneer Research Program, I worked with Professor Amir Rasheed of Amherst College. I explored knot theory, a branch of topology that studies mathematical knots and the properties that remain unchanged under continuous deformation.

My research focused on knot invariants, including tricolourability, Fox colouring, the Alexander polynomial, and knot determinants. I investigated how these invariants behave under connected sums, examining the multiplicative relationship between the determinants of composite knots and their constituent knots.