Khovanov homology and rationnal unknotting

Khovanov homology is a powerful link invariant introduced around 2000 as a categorification of the Jones polynomial. It started a rich field of study that proved to have surprising applications in various areas of knot theory and topology. In this talk, we will use Khovanov homology to extract a new link invariant λ. While λ is a lower bound for the unknotting number, in fact more is true: λ is a lower bound for the proper rational unknotting number, i.e. the minimal number of connectivity preserving rational tangle replacements needed to make a knot trivial. Along the way we will compute the Khovanov chain complexes of rational tangles. This is based on joint work with Damian Iltgen and Lukas Lewark.