Kylerec 2019

Topic: Sheafy symplectic topology

Date: May 31 – June 6, 2019

Location: Truckee, CA

Flyer: Available here.

Applications are open ! Please complete this form by March 22nd, 2019. 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.

Description: 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 infinitesimal 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, generalizing 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 of 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, as well as more advanced graduate students.

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 the 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. There are no spectators, only participants!

Pre-workshops: Leading up to the main workshop, smaller pre-workshop will be organized. Stay tuned for more details !

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

Organizing committee: Orsola Capovilla-Searle (Duke), Dahye Cho (Stony Brook), Cédric De Groote (Stanford), Tim Large (MIT), Sarah McConnell (Stanford).

Funding: We are grateful to the NSF for their support. Local expenses (including lodging and food) and partial travel expenses will be covered for participants.

Contact: You are welcome to ask any questions by sending an email to kylerec2019@gmail.com.

Past Workshops: For the webpages from the previous Kylerec workshops, see the following pages.

2018 Kylerec on the nearby Lagrangian conjecture

2017 Kylerec on symplectic fillings

2016 Workshop on Lefschetz fibrations: rigidity and flexibility

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