"I propose to pursue several independent studies in symplecticgeometry and Hamiltonian dynamics. My research objectives aretwofold. First, to solve some of the open research questionsdescribed in the proposal, which I consider to be pivotal in the field.Some of these questions have already been studied intensively, andprogress toward solving them would be of considerable significance.Second, the proposed research is closely tied to other fields suchas convex geometry and asymptotic geometric analysis (Problem 1.1and 1.2), algebraic geometry and mirror symmetry (Problem 1.4), andthe theory of mathematical billiards (Problem 1.3). Theseconnections have already proved fruitful in tackling questions thatwere out of reach for common symplectic methodology thus far, and Iexpect further significant results to be within reach. Moreover,partly due to these ties, this research has a wide range of possibleapplications outside of symplectic geometry. Therefore, my secondresearch objective is to utilize the suggested questions in order todeepen and broaden the connections between symplectic geometryand the above mentioned fields."