  In this report, I will start by first giving a brief introduction on knots to
build some intuition before beginning the more rigorous review in the
Literature Review section. There, I will define knot equivalence, the Jones
polynomial invariant, braid groups, Hecke algebras, and the HOMFLY polynomial
invariant. Next, I will cover some of my independent research regarding the
computation of a general formula for the HOMFLY polynomial of the closure of
looped coxeter braids. Lastly, I will loosely discuss how this research
connects to future research regarding the universal trace in the Plan for
Future Work section.
