Kylerec 2018

KYLEREC 2018 is now over. All notes can be found by visiting this page!


Topic: Cotangent bundles and the nearby Lagrangian conjecture

Date: May 25 – 31, 2018.

Location: The Leavenworth Lodge, Washington State, USA

Flyer: You can find our flyer here!

Description: The topic this year is the nearby Lagrangian conjecture, stating that every closed exact Lagrangian L in a cotangent bundle T*is Hamiltonian isotopic to the zero-section. We will look at this via the work of Thomas Kragh, proving that the projection of the Lagrangian to the base of the cotangent bundle is a homotopy equivalence. This work is accessible to beginner students, and worthwhile to learn for more advanced students. We will spend some time on the wrapped Fukaya category, one of the most important tools in the subject and reasonably tractable here. Proving the homotopy equivalence from the homology equivalence is then a great opportunity to learn about local systems in Floer theory, and about how they can be used to encode homotopical information. Finally, we plan to look at proofs of the conjecture in low dimensional cases, in particular for the cotangent bundles of exotic spheres. These provide beautiful examples of how a delicate study of moduli spaces of pseudo-holomorphic curves can produce stunning results in symplectic geometry. For more mathematical info, click here!

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 participants, with guidance from our mentors. Our vision is to curate 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, two smaller pre-workshops were organized. There was one held at Stanford University on May 5, and another will be held at Columbia University on May 12. Notes from both are available.

Mentors: Roberta Guadagni, Thomas Kragh, Kyler Siegel, Jingyu Zhao

Organizing committee: Catherine Cannizzo, Orsola Capovilla-Searle, Cédric De Groote, Tim Large, Kevin Sackel

Funding: We are grateful to the NSF for their support under Grant DMS-1818138.

Applications: Applications are now closed.

Contact: You are welcome to ask any questions by sending an email to

Past Workshops:

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

2017 Kylerec on symplectic fillings

2016 Workshop on Lefschetz fibrations: rigidity and flexibility