This $300,000 Project Grant awarded by the National Science Foundation (NSF) Mathematical and Physical Sciences (MPS) program supports fundamental research in quantitative symplectic geometry and dynamics at the University of California, Berkeley. The project aims to develop new mathematical tools to study the evolution of physical systems over time, with a focus on understanding the properties of periodic orbits in four-dimensional phase spaces. The research involves several specific projects investigating topics such as embedded contact homology, symplectic cobordisms, symplectic invariants, and closing lemmas. The funding will provide research training for graduate students and engage in outreach activities. No sub-awards are planned under this grant, which has an award period from August 1, 2024 to July 31, 2027.
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