# Mathematics Colloquia and Seminars

In 1997 Chekanov gave the first example of a knot type whose Legendrian representations are not distinguishable using only the classical invariants: the $5_2$ knot. Epstein, Fuchs and Meyer extended his result by showing that there are at least $n$ different Legendrian representations of the $(2n+1)_2$ knot with maximal Thurston-Bennequin number. The aim of this talk to give a complete classification of Legendrian representations of twist knots. In particular the $(2n+1)_2$knot has exactly $\lceil \frac{n^2}{2} \rceil$ Legendrian representations with maximal Thurston-Bennequin number. This is a joint work (in progress) with John Etnyre and Lenhard Ng.