USC Topology Seminar: Cluster algebras and Legendrian 3-braids

Event details Date: Monday, September 14, 2026 Time: 2:00 PM to 3:00 PM Location: Kaprielian Hall (KAP) - 265 - 3620 South Vermont Avenue, Los Angeles, CA 90089 Type: Lecture / Talk / Workshop Campus: University Park Campus Department: Mathematics About this event James Hughes, USC Title: Cluster algebras and Legendrian 3-braids Abstract: Given a Legendrian link L in the standard contact 3-sphere, one can hope to classify the set of exact Lagrangian fillings of L, i.e. exact Lagrangian surfaces in the symplectic 4-ball with boundary equal to L. Much of the recent progress towards this classification problem relies on establishing a connection between cluster algebras and various algebraic analogs of a moduli of Lagrangian fillings. In this talk, I will describe this connection and highlight some new phenomena that occur in the case of Legendrian 3-braid closures. This talk is based off of joint work in progress with Lenny Ng and Daping Weng. Official event details: https://calendar.usc.edu/event/usc-topology-seminar-cluster-algebras-and-legendrian-3-braids