Marco Marengon

Given a knot in the 3-sphere, one can associate some knot homologies with it, among which knot Floer homology and (reduced) Khovanov homology.
Motivated by Fox-Milnor's obstruction for slice knots, we prove that all knots in a certain family have these homologies with total rank being a square integer.
Moreover, we conjecture that the rank of knot Floer homology is congruent to 1 modulo 8 for all slice knots, and we prove this fact for a subfamily of slice knots, namely fusion number 1 ribbon knots.
This is a joint work with Hockenhull and Willis, and partially also with Dunfield and Gong.