Robert John Quarles

Current Projects

My current research deals mainly with a polynomial time knot polynomial, defined by Dror Bar-Natan and Roland van der Veen, which is a simple, strong knot invariant that is closely related to the Alexander polynomial.  In my work I prove how the invariant acts under the connected sum  operation,  give  a state  sum  formulation  for  the  invariant,  and explore  how  to  build the invariant from a set of smaller pieces (giving the explicit construction for the family of T(2,2n+1) torus knots).