Current Trends in Symplectic Topology

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A summer school on "Current Trends in Symplectic Topology" will be held at the CRM (Centre de Recherches Mathematiques) in Montreal from July 1-12, 2019. Symplectic topology is a rapidly developing branch of geometry that has seen phenomenal growth in the last twenty years. The school is intended to provide access to this subject to a diverse group of graduate students and postdoctoral researchers. The school will consist of minicourses by leading researchers in the field, exercise sessions, selected talks by young researchers, and an open problems panel to identify central directions for future research. The grant will provide funding to enable US-based graduate students and postdoctoral researchers to participate in the summer school. This will improve the US workforce by providing training in important cutting-edge research topics.Major themes to be covered in the summer school are the dichotomy between rigidity and flexibility; the Fukaya category and homological mirror symmetry; Hamiltonian dynamics, capacities, and spectral invariants; symplectic field theory, its variants, and applications; and foundational properties of moduli spaces of J-holomorphic curves. Although there have been some recent specialized conferences on individual topics in the above list, the summer school is unique in synthesizing these different aspects of symplectic topology into an overview accessible to young researchers.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.