The Kinoshita-Terasaka and Conway knots are notoriously hard to distinguish. This is because they are related by mutation, an operation on knots that has subtle geometric effects. Many classical and modern knot invariants cannot tell mutants apart. In this talk, I will discuss how various flavors of knot Floer homology detect and/or fail to detect mutations. The main result is a partial proof of Baldwin and Levine's conjecture that Conway mutation preserves delta-graded knot Floer homology. Speaker(s): Peter Lambert-Cole (Indiana University)