Abstract
The meridional rank conjecture asks if the minimal number of meridians needed to generate the knot group of a knot K is equal to the bridge number of K. The question was originally posed by Cappell and Shaneson in the 1970s. In this talk, we will introduce an alternative definition of bridge number known as Wirtinger number. By combining Wirtinger number and Coxeter quotients of knot groups, we will establish the meridional rank conjecture for several classes of knots. We will also discuss computational results in which we apply these techniques to all tabulated prime knots with at most 16 crossings
