Mathematics Colloquia and Seminars

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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.