This award supports a five-day conference titled Lagrangian Floer Theory and Applications to be held September 28--October 2, 2026, at the Center for Mathematical Sciences and Applications in Cambridge, Massachusetts. The meeting is organized by Chris Woodward (Rutgers) with the assistance of Denis Auroux (Harvard) and Jonny Evans (Lancaster). Lagrangian Floer theory arose from research on Hamiltonian dynamics, which is the mathematical study of such systems as the motion of the planets. In recent years, Floer theory has become connected to quantum invariants in topology. The meeting will bring together experts at the frontier of research in these areas from around the world. The conference is expected to generate transfers of knowledge, new collaborations, and a cross-fertilization of ideas, and further inspire graduate students and early-career mathematicians. The web-page for the workshop is https://cmsa.fas.harvard.edu/event/lftworkshop/. The scientific themes of the event include applications to dynamics and classification problems; connections with singularity theory; mirror symmetry and tropical techniques; categorical aspects; and Floer homotopy theory. Each day of the meeting will focus on one of these themes. There will be approximately 25 invited speakers, with each speaker giving a one-hour talk. The list of speakers includes two graduate students, five postdoctoral researchers, and five tenure-track assistant professors. The speakers come from small liberal arts colleges, distinguished public and private research universities, and highly regarded international research institutes and universities. The award supports invited speakers, and participants who are U.S.-based graduate students or postdoctoral fellows. 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.