I am currently supervising a group of undergraduate students in a project run through the Illinois Math Lab at UIUC. We are investigating a botany problem for non-orientable surfaces with boundary a given knot K. Our goal is to use Khovanov homology to help find two distinct Mobius bands in B^4 with normal Euler number -6 and boundary the (2,5) torus knot. We have a conjectured pair of Mobius bands and we hope to be able to show that they induce distinct maps on Khovanov homology.
The botany problem for non-orientable surfaces is a fairly uninvestigated topic and there are many simple questions and a dearth of examples. I hope to continus this research in future projects.