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Geometry and Topology Seminar - A Distance Function on Smooth Families of Embeddings

Joey Palmer, Department of Mathematics, Washington University in St. Louis

March 22, 2013 - 4:00 pm to 5:00 pm
Location: Cupples I, Room 199 | Host: Prof. Xiang Tang

Abstract: It is a recent theorem of Pelayo and Vu Ngoc that given a smooth family of symplectic embeddings from subsets of a manifold M into a manifold N satisfying a few additional hypotheses there always exists a symplectic embedding from the union of their domains into N. This result was used to prove the nonexistance of intermediate symplectic capacities, and in this talk we will explore the first steps to gaining a greater understanding of their result, with the hope of applying it to a broader range of problems. With this in mind, we introduce a distance function on the collection of embeddings from subsets of M into N and discuss its properties.