There are many ways to draw spheres and tori into four dimensions in a way that they are “knotted.” It is not easy to imagine (or even draw) a knotted sphere in dimension four. In this talk, we will discuss two ways to represent such surfaces using ideas of knot theory in dimension three. We will discuss how to color these descriptions to obtain new invariants of knotted surfaces in 4-space. This is joint work with Nicole Marienau, Erica Pearce, Savannah Schutte, and Ransom Sterns.

This talk will discuss the student findings of the most recent iteration of MATH 398 - Research Experience in Mathematics at UNL.