Conference: Southern California Symplectothon

University Of Southern California, Los Angeles CA

Investigators

Abstract

The Southern California Symplectothon is an annual intensive learning multiday retreat for Southern California geometers which will take place in fall 2025 and fall 2026, with the upcoming workshop slated to take place at the University of Southern California Wrigley Marine Science Center in Avalon, CA. Participants will meet over a long weekend to learn about and disseminate important new developments in geometry and topology, with a special focus on symplectic geometry and adjacent areas. The Symplectothon will also make a concentrated effort to build the local regional network, by forging and strengthening in-person bonds and potential collaborations. Each Symplectothon workshop will focus on a specific emerging topic, and participants will typically consist of 20-30 graduate students, postdocs, junior faculty, and senior faculty from an array of institutions in the greater Southern California region. There will be one or two in-person invited experts and a similar number of virtual invited experts. Participants will stay together in a single dedicated location, and talks will be given by the participants, with plenary lectures by the invited experts. Each Symplectothon will also include several guided discussion and Q+A sessions, as well as a forward-looking talk on future directions by one of the invited experts. Outside of the intensive scientific programming schedule, participants will have ample time for open discussions, while building personal and professional ties through social activities such as collective cooking, hikes, and other outdoor activities. The chosen topics for Symplectothon 2025 include Lagrangian fillings and cluster algebras. Participants will learn about Lagrangian fillings of Legendrian knots, cluster algebras, and microlocal sheaves, culminating in recent deep connections between these, particularly the work of Casals–Gao which establishes the existence of Legendrian knots with infinitely many distinct Lagrangian fillings and separately shows that every cluster seed in the augmentation variety arises from a Lagrangian filling. This is an exciting and interdisciplinary area under active development, and Symplectothon 2025 will be designed to bring Southern California geometers up to the research forefront. It will create an opportunity for researchers from different scientific backgrounds (i.e. symplectic geometry and cluster algebras) to convene and learn from each other. The participants will also learn about and discuss many other potential applications, such as the recent construction of cluster structures on braid varieties using ideas from symplectic topology, as well as many possible future connections between symplectic topology and cluster algebra. The tentatively chosen topic for Symplectothon 2026 is "tropical curve counts beyond toric geometry". A dedicated Symplectothon website with application information, syllabi, and typed lecture notes will be maintained at https://kylersiegel.xyz/symplectothon.html. 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.