Speaker: Dr. Byung Hee An (IBS-CGP)
Date: June 4th, 5:00-6:00 PM
Place: AORC Seminar Room (SKKU, General Studies Bd. 3F)
Title : Augmentation varieties and cluster algebras for Legendrian (2,n) torus knots
Abstract :
For a Legendrian knot, one can associate a differential graded algebra(DGA), and any embedded exact Lagrangian filling of the knot provides an augmentation of the associated DGA.
On the other hand, the space of augmentations forms an algebraic variety, called the augmentation variety. In this talk, we will provide the family of open charts for the augmentation variery of the Legendrian (2,n) torus knot, which are indexed by the set of faces of the associahedron of type An. Moreover, each chart can be realized as the deformation space of the constructible Lagrangian filling.
If time permits, we will discuss the possible generalization for E6 and E8 cases.