American Institute of Mathematics, Palo Alto, California
Dmitry Fuchs, Serge Tabachnikov, and Lisa Traynor
One of the main goals of the workshop is to achieve a better understanding of a somewhat mysterious combinatorial structure of front diagrams of Legendrian knots, the so-called, normal rulings. This structure is closely related to seemingly independent properties of Legendrian knots: the existence of generating families of functions, certain algebraic properties of the Chekanov--Eliashberg algebra (augmentations), and the sharpness of the estimates of the self-linking (Thurston--Bennequin) numbers of Legendrian knots. A second goal is to make progress in the study of transverse knots, in particular, by constructing transverse invariants of the contact homology type. Further goals include applying Legendrian knot theory to topological knot theory and finding applications of Legendrian knot theory to global singularity theory in the spirit of Chekanov and Pushkar�s recent proof of Arnold's four cusps conjecture.
The workshop schedule.
A report on the workshop activities.