Thursday 5th of October 2023, 13:30-14:30 in LIN6
Chris Pirie
Quotients in Symplectic Geometry.
A natural question in geometry is whether the quotient of some geometric object by a group action inherits, canonically, said geometric structure. For example, the quotient manifold theorem from differential geometry states under what conditions the quotient of a smooth manifold is also a smooth manifold, namely a free and proper action. In this talk we discuss the difficulties in trying to take quotients in symplectic geometry, and how to rectify such issues. This will lead to the idea of symplectic reduction, or the Marsden-Weinstein-Meyer theorem. Time permitting, we also explain how most of the conditions on reduction can be removed if we allow singularities.