Unknotting numbers and satellite operations

A natural measure of complexity for knots is the unknotting number - roughly how many over crossings changed to under crossings are needed to unknot a knot. The unknotting number is poorly understood for most general constructions in knot theory, including connected sums. We will discuss some new lower bounds on the unknotting numbers of a large family of knots, called cable knots. This is joint work with Jen Hom and Jung Park.