The field of symplectic geometry historically arose from classical mechanics, where symplectic manifolds provide a natural geometric framework in which to discuss Newton’s equation of motion. In fact, a vast variety of physical processes – from planetary motions in celestial mechanics, to interactions of complex quantum fields – can be described as Hamiltonian dynamical systems, and consequently treated with symplectic tools. Over the past three decades, due in part to motivating questions from theoretical physics, symplectic geometry has evolved into a major research field, and nowadays, symplectic geometry combines a broad spectrum of interrelated disciplines lying in the mainstream of modern mathematics.
The SYMPLECTIC project is composed of several studies in symplectic geometry and Hamiltonian dynamics on topics related to symplectic embedding questions, the geometry of the group of Hamiltonian diffeomorphisms, Lagrangian rigidity questions, and the theory of symplectic measurements. The project’s objectives are twofold. First, to solve several open research questions, which are consider to be pivotal in the field of symplectic geometry. Some of these questions have already been studied intensively, and progress toward solving them would be of considerable significance. Second, some of the studies in this proposal are interdisciplinary by nature, and use symplectic tools in order to address major open questions in other fields, such as the famous Mahler conjecture in convex geometry. The project aims to deepen the connections between symplectic geometry and these fields, thus creating a powerful framework that will allow the consideration of questions currently unattainable.
