Gordian distance bounds from Khovanov homology

The Gordian distance u(K,K') between two knots K and K' is defined as the minimal number of crossing changes needed to relate K and K'. The unknotting number of a knot K, a classical yet hard to compute knot invariant, arises as the Gordian distance between K and the trivial knot. Several lower bounds for both invariants exist. A well-known bound for the unknotting number is given by the Rasmussen invariant, which is extracted from Khovanov homology, a bigraded chain complex associated to a knot up to chain homotopy equivalence.
In this talk, I will introduce a new lower bound for the Gordian distance, \lambda, coming from Khovanov homology. After introducing all the relevant ingredients, I will present some results about \lambda. In particular, \lambda turns out to be sharper than the Rasmussen invariant as a lower bound for the unknotting number. This is based on joint work with L. Lewark and C. Zibrowius.