New Invariants for Legendrian Knots

Jill Jordan

Spaces with a contact structure naturally arise in the study of geometric optics and control theory. In these spaces, curves with certain characteristics are called Legendrian knots. The geometric structure of the space imposes restrictions on the movements of the knots, and a fundamental question is to understand when one knot may be moved to another knot. There are some classical ways to show that two Legendrian knots are different, and I am working on finding new ways.