Georgia Institute of Technology College of Sciences

A knot can be thought of as a piece of string tied up, that then has its ends glued together. As long as we don’t cut the string, any way we move the string in space doesn’t change the knot we are considering. A surprisingly hard and interesting problem is, when handed two knots, how to determine if they are the same knot or not. We can further give structure to our knots and thus the problem, by adding geometric constraints to our knots, yielding what are called Legendrian knots. We can once again try to determine if two Legendrian knots are the same or not. In this talk I will introduce knots, Legendrian knots, and some ways we have to try to distinguish two knots or Legendrian knots, called knot invariants.