Slicing knots in general 4-manifolds

Knots which bound embedded discs in the 4-ball are called slice, and such knots have been studied for several decades. More generally one can ask which knots bound embedded discs, i.e. are slice, in an arbitrary 4-manifold with 3-sphere boundary. E.g. if one finds a knot which is slice in a homotopy 4-ball but not in the 4-ball, this would disprove the 4-dimensional Poincare conjecture. In this talk I will discuss recent work in this area, including but not limited to my joint work with Kasprowski, Powell, and Teichner; with Miller, Kjuchukova, and Sakalli; and with Marengon, Miller, and Stipsicz. I will also state some of my favourite open problems in this topic.