RTG Colloquium

Michael Usher (U Georgia)
Symplectic embedding questions via Morse and Floer theory


The phase space of a physical system---parametrized by the position and momentum coordinates of its constituent particles--evolves according toa special kind of geometric transformation known as a symplectomorphism.  Beginning with Gromov's non-squeezing theorem in the 1980s, it has come to be understood that the seemingly simple question of when one region in R^{2n} embeds via a symplectomorphism into another region has an answer that depends surprisingly subtly on the regions involved. A similar remark applies to the question of whether any two such embeddings are equivalent in an appropriate sense.  I will survey a variety of results by various authors concerning instances of these problems, focusing on the use of algebraic structures inspired by Morse theory that are associated to star-shaped subsets of R^{2n}.

Followed by technical talk/seminar the following day 11/4 2:30-3:30 in 214 MLH.

Event Date: 
November 3, 2021 - 3:30pm to 4:30pm
113 MLH
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