Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

The Legendrian contact DGA (differential graded algebra) is a fundamental invariant of Legendrian submanifolds that is functorial for a class of Lagrangian cobordisms. In particular, a Lagrangian filling of a Legendrian knot induces an augmentation, i.e. a DGA map $\mathcal{A}(\Lambda) \rightarrow \mathbb{F}$ to a base field. It is natural to ask: Can every augmentation be induced by a Lagrangian filling?. The answer is no, and we will survey known obstructions to inducing augmentations by fillings and give some new examples (joint with H. Gao) of non-fillable augmentations of Legendrian twist knots. We will then present a complementary result (joint with Y. Pan) showing that any augmentation can in fact be induced by an \textit{immersed} Lagrangian filling. Time permitting we will discuss (joint work in progress with H. Gao) examples of immersed fillings related to ruling stratifications of augmentation varieties.