UBC Math Department Colloquium: Liam Watson

Mutation is a process that makes a non-trivial local change to a knot; the distinction between the resulting pair of knots is difficult to detect. I will present a vaguely historical account of why mutant pairs are difficult to distinguish. This will focus on symmetries of certain relative invariants associated with Khovanov homology: I will explain why Khovanov homology cannot detect mutation, but that in certain instances, the presence of an appropriate involution gives way to a new refinement of Khovanov homology that is able to separate mutant pairs.