• Speaker: Aliakbar Daemi
• Time: 9:30-10:30
• Abstract: Following Arnold and Hormander, generating functions can be used to produce an important family of immersed Lagrangians in the cotangent bundle of a manifold M and Legndrians in the 1-jet space of M. In this talk, I’ll give a report on a joint work with Kenji Fukaya where we study Lagrangain Floer homology (resp. Legendrian contact homology) of such Lagrangians (resp. Legendrians). In particular, we show that such Lagrangians admit bounding chains and we compute the Lagrangian Floer homology groups defined with respect to such bounding chains. On the Legndrian side, part of this result can be interpreted as an existence result for augmentations of Legnedrians, generalizing earlier works on 1-jet space of 1- and 2-dimensional manifolds to arbitrary dimensions. As an application of these results, one obtains topological lower bounds on the number of Reeb chords of Legendrians induced by generating functions, in the same sprit as Arnold conjecture for Legendrians.