國立清華大學 數學系

Symplectic maps are geometric mappings that preserve the structure of a mechanical system. Symplectic topology is the subject of the study of topological problems under symplectic maps, or equivalently of the "globalization" of the geometry of classical mechanics. It turns out to lie in the common intersection of quantum physics, dynamic systems and topological data analysis. In this colloquium style talk we will mention some interesting phenomenons for symplectic maps and various symplectic topology problems will be given. If time permits, we will want to emphasize the relation between symplectic squeezing problem, Heisenberg uncertainty principle, and Hofer geometry.