Title: Moser's Trick and the Darboux Theorem in Symplectic Geometry
Abstract: Suppose M is a compact, oriented manifold with two volume forms whose integral over M is equal, can we find a diffeomorphism, M to M, that relate the two forms via pullback. We can use Moser's trick to prove this statement and some other similar statements in symplectic geometry. The trick involves isotopies and time-dependent vector fields which I will introduce, "prove" a few facts about, and then use to show the first statement. I will then briefly introduce symplectic manifolds, and sketch the proof of Moser's Relative Theorem. Time permitting, I will show how the Darboux Theorem follows from Moser's Relative Theorem.
Note: The talk will start at 4:10 pm
Daniel Mallory
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