Research

My research interests are primarily on constructive techniques in low dimensional topology, particularly knotted surfaces. The double slicing problem, and the problem of surface slicing in general is of particular interest to me.

Open problems that are of particular interest to me are:

The Slice-Ribbon Conjecture

Finding a 3-manifold embeddable in a homology 4-sphere but not the 4-sphere (I solved this one!)

Finding a knot that is slice in a homology 4-ball but not in the 4-ball

Finding a knotted projective plane in the 4-sphere that does not decompose as an unknotted plane and a knotted sphere (the Kinoshita Conjecture)

Proving that Gluck twists on certain families of 2-knots are standard 4-spheres