Expanders: Knots, metrics and graphs

I will discuss the existence of sequences of bounded curvature metrics on the d-dimensional sphere (d>2) whose volume tends to infinity but
whose Cheeger constant is uniformly bounded from below by a positive constant. As a consequence, it follows that there are sequences of
hyperbolic knot complements with again volume tending to infinity and Cheeger constant uniformly bounded from below. Joint work with Marc
Lackenby.