Seminar: Knot Mosaics on Interesting Surfaces
Speaker: Samantha Pezzimenti, Widener University
Abstract: In this talk, we will explore a handful of recent projects, all related to knots and all joint with undergraduate students. A mathematical knot can be thought of as a tangled loop of string with its ends attached. One convenient (and beautiful) way to construct knots is by arranging a set of mosaic tiles into a square grid. These knot mosaics are useful in tabulating knots and defining invariants, such as the mosaic number, and lead to interesting research questions. What if we allow the mosaic to be built on a cube? On a torus? On a cylinder or Mobius band? What if we impose some requirements on the knot structure? These questions all lead to interesting and surprising results!
Host: Martha Precup