Symmetric knots and the equivariant 4-ball genus

Given a knot K in the 3-sphere, the 4-genus of K is the minimal genus of an orientable surface embedded in the 4-ball with boundary K. If the knot K has a symmetry (e.g., K is periodic or strongly invertible), one can define the equivariant 4-genus by only minimising the genus over those surfaces in the 4-ball which respect the symmetry of the knot. I'll discuss ongoing work with Keegan Boyle trying to understand the equivariant 4-genus.