Student Geometry/Topology Seminar

A natural question in symplectic geometry is when there exists an embedding from one symplectic manifold into another that preserves the symplectic structure. This question is surprisingly difficult, because symplectic geometry exhibits a strange blend of rigidity and flexibility that is only partially understood. For this reason, embedding results are only known for a few simple manifolds. I will begin by explaining how these problems are closely related to the time evolution of a mechanical system. I will then survey some known results about embedding some simple symplectic manifolds. This leads to an interesting combinatorial/number theoretic problem. If time permits, I will discuss a connection with the Uncertainty Principle. This talk will feature much of the same vocabulary and setup as my talk from last semester. Speaker(s): Daniel Irvine (University of Michigan)