Abstract: A central question in symplectic geometry is to determine which symplectic manifolds are symplectomorphic. We provide novel tools to answer this question in a new context: We use time-independent incomplete Hamiltonian flows to excise interesting closed subsets of positive codimension from symplectic manifolds. In this talk I will focus on our reduction of this symplectic question to a differential-topological question. In tomorrow's colloquium I will discuss this differential-topological question, but the two talks will be independent of each other. This is joint work with Xiudi Tang, available on the arXiv.