Toward a contact Fukaya category

Thursday, February 11, 2016 -
1:00pm to 2:00pm
Please note special time.  I will describe some work in progress (maybe more accurately, wild speculation) regarding a version of the derived Fukaya category for contact 1-jet spaces J^1(X). This category is built from Legendrian submanifolds equipped with augmentations, and the full subcategory corresponding to a fixed Legendrian submanifold \Lambda is the augmentation category Aug(\Lambda), which I will attempt to review. The derived Fukaya category is generated by unknots, with the corollary that all augmentations ``come from unknot fillings''. I will also describe a potential application to proving that ``augmentations = sheaves''. This is work in progress with Tobias Ekholm and Vivek Shende, building on joint work with Dan Rutherford, Vivek Shende, Steven Sivek, and Eric Zaslow.
Lenny Ng
Duke University
Event Location: 
IAS Room S-101