Ben studies Advanced Science with Honours at Monash University. He has finished his double major in maths, and is completing his honours in commutative algebra in 2015. He is interested in algebra and geometry, and has completed research projects in both symplectic geometry and permutation puzzles. Outside of maths, Ben enjoys Rubik’s cube puzzles and video games, and has held positions on five committees for Monash student clubs. His project looks at relationships between knot invariants and representation theory.
The Interplay between Knots and Representations
A knot is made by taking a piece of string, tying it up in some fashion, and then gluing the ends together. For well over a century, mathematicians and scientists have been preoccupied with the question of how to distinguish two given knots. Over the past three decades, inspirations from algebra and theoretical physics have led to a vast theory of knot polynomials, which help to answer this question.There is much recent work in the knot theory literature that highlights the interplay between knots and representations. A representation is a way to encode an algebraic structure, such as a group, using matrices. This project will examine this fascinating interplay via explicit computations.