Removing double points of surfaces in 4-manifolds via multi-tubing

In joint work with Marco Marengon we present a simple but flexible
method to simultaneously remove multiple double points of immersed
surfaces in 4-​manifolds. One consequence is that in an appropriate
sense many knots bound disks in 4-​manifolds, and in particular, we
significantly improve the best known bound in the K3 surface. Namely,
for a small 4-ball in K3, we show that all unknotting number 21 knots on
its boundary 3-sphere will bound disks in the interior of K3. In work in
progress in a different direction I aim to improve upper bounds on the
minimal genus function in some 4-manifolds, an important smooth
invariant generally hard to pinpoint.