Conference: Kylerec Student Workshops in Symplectic and Contact Geometry

The 2025 edition of the Kylerec Graduate Student Workshop is scheduled to take place during the period June 23-27, 2025, near Tahoe, CA, and this award provides support for the next three editions of the workshop (2025, 2026 and 2027). The Kylerec workshop aims to introduce aspiring mathematicians in the fields of symplectic and contact geometry and from many institutions to vibrant areas of research, fostering collaboration, forming strong research ties between young researchers, and thus promoting future collaboration and research.

The workshop is specifically designed to encourage the development of a diverse group of researchers in the fields of symplectic and contact geometry. It is a week-long intensive workshop, in which all activities occur under one roof which serves as the mathematical and social center for the week. The lectures are delivered by the graduate student participants with the help of three or four mentors, who are early career researchers and emerging experts in the field.

This setup enhances communication skills, encourages active involvement of the participants and forging new collaborations. Participants also cook, clean and eat together, further fostering the sense of community.

The planned topic for the 2025 Kylerec workshop is Floer homotopy theory, focusing on the emerging subject of lifting constructions in symplectic Floer theory to the level of stable homotopy theory, and applications to classical problems in symplectic geometry such as the classification of exact Lagrangian submanifolds or the study of Hamiltonian fibrations and families of symplectic manifolds. Ever since Floer's original breakthrough on the Arnold conjecture, constructions of Floer-type theories of increasing complexity were introduced with tremendous success for applications in symplectic topology, such as the recent Abouzaid–Blumberg result on the Arnold conjecture with mod p coefficients.

The objective of the Kylerec workshop is to understand the current state of the art in these topics, including both the technical tools utilized and the applications, as well as some of the broader philosophy that has come out of the work on these topics. Along the way, we hope that participants will encounter a wide variety of different ideas coming from the various approaches, as well as exciting new areas and open problems stemming from the recent developments. Kylerec workshops website: https://kylerec.wordpress.com/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.