Kylerec 2019

Applications have opened for Kylerec 2019, a student workshop in symplectic geometry and contact topology happening in California this summer.

The topic for Kylerec 2019 is “Sheafy Symplectic Topology”.

Graduate students at any stage are encouraged to apply. We especially encourage applications from women, underrepresented minorities, and we are committed to providing assistance to students with disabilities or special needs. We are grateful to the NSF for their support. Local expenses (including lodging and food) and partial travel expenses will be covered for participants.

Applications due by March 22nd. Please apply at this link https://form.jotform.com/90358074641155 

Format: Kylerec is a student-led and student-run workshop. We will live in a communal setting, sharing cooking and cleaning responsibilities. Talks will be given by a majority of participants, with guidance from our mentors. Our vision is to foster a healthy, relaxed and creative atmosphere where we can learn mathematics together and make human connections in the process.

Topic: This year, we will investigate the relationship between the Fukaya categories of exact symplectic manifolds and sheaf theory. Fukaya categories are a central part of modern symplectic topology, mirror symmetry and low-dimensional topology, however they remain very difficult to compute. On the other hand, categories of constructible sheaves are much more concrete and tractable. In the case of a cotangent bundles, the work of Nadler-Zaslow identifies the wrapped Fukaya category with a certain category of sheaves on the zero-section. For more general Weinstein manifolds, it is conjectured that one can find a Lagrangian skeleton, generalising the zero-section of a cotangent bundle, with at worst singularities from Nadler’s “arboreal” list. The wrapped Fukaya category is then expected to coincide with a category of sheaves on this skeleton. In particular, this suggests Fukaya categories should themselves exhibit “sheafy” properties: they might be reconstructed by breaking a symplectic manifold into pieces and gluing together local computations. One approach to doing this is provided by the work of Ganatra-Pardon-Shende, with many important structural implications for wrapped Fukaya categories.

This workshop will survey this circle of ideas. After covering the basics of Floer theory, the Fukaya category and sheaf theory, we will delve into the work of Nadler-Zaslow and Ganatra-Pardon-Shende. We hope to see lots of interesting examples, calculations and applications along the way, in particular the aforementioned arboreal singularities. This should be of great interest to both newcomers to the symplectic and contact geometry, and more advanced graduate students.

Mentors:  Sheel Ganatra (USC), Xin Jin (Boston College), Laura Starkston (UC Davis), and Umut Varolgunes (Stanford).

Dates: May 31-  June 6, 2019

Location: Truckee CA (near Lake Tahoe)

For further questions, please email kylerec2019@gmail.com

More information is available at https://kylerec.wordpress.com/

Kylerec Workshop kylerec.wordpress.com All notes are courtesy of Cédric De Groote! You can either view them: In two parts (including notes from the West Coast Pre-Workshop): Part_1 Part_2 Lecture-by-lecture.