This talk will describe some recent work with two undergraduates at Bryn Mawr College (Sumana Shrestha '06 and Cristina Nistor '05) on Legendrian knot theory. Legendrian contact homology, which is a relative version of Eliashberg-Givental-Hofer's Symplectic Field Theory, is a powerful new tool in the subject. A combinatorial - albeit unwieldy - version of the theory was formulated by Chekanov a few years ago, and by using a linearization of this theory he produced the first examples of distinct knots with the same "classical invariants". Based on computational evidence, it was conjectured by Lenny Ng and others that this linearization is unique. Our work addresses this conjecture, but you'll have to come to the talk to find out how.