College of Liberal Arts & Sciences

# RTG Colloquium

**Abstract:**

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.