Claremont Topology Seminar: Morgan Weiler (University of California, Riverside)

We especially welcome all undergraduates and graduate students to attend topology seminar!

Speaker: Morgan Weiler (University of California, Riverside)

Title: Anchored symplectic embeddings and 2-parameter persistence

Abstract: Symplectic geometry is a generalization of classical mechanics, in which position and momentum coordinates are paired. In two dimensions, symplectic geometry is equivalent to volume-preserving geometry, but in higher dimensions, Gromov proved in volume inequality is not enough to guarantee embedding. In this talk, we will explain an example for which requiring the complement of the embedding to contain a symplectic surface with fixed boundary conditions (the so-called “anchor”) provides an even stronger restriction than the symplectic form alone. The result is joint work with Michael Hutchings, Agniva Roy, and Yuan Yao; the method of proof that will be shown is ongoing work with Hutchings, Roy, and Yao and uses 2-parameter persistence modules, a tool from topological data analysis which we will review.