Conway mutation in knot Floer, Khovanov and Bar-Natan homology
Conway mutation is an operation on links that is notoriously difficult to detect: it preserves many classical link invariants such as the Alexander polynomial and the Jones polynomial. How the corresponding link homology theories behave under mutation is still a question of active research. In this talk, I will discuss some progress that has recently been made in this area using certain immersed curve invariants for 4-ended tangles, which put these homology theories locally on an equal footing. This is in large parts joint work with Liam Watson and Artem Kotelskiy.