Khovanov homology detects the trefoils

In 2010, Kronheimer and Mrowka proved that Khovanov homology detects
the unknot, by constructing a spectral sequence from reduced Khovanov
homology to a form of instanton knot homology and then showing that
the latter has rank 1 only for the unknot.  In this talk, we will
discuss joint work with John Baldwin in which we apply techniques from
contact geometry to prove that the rank of instanton knot homology
also detects the trefoils.  As a corollary, we conclude that Khovanov
homology is also a trefoil detector.