February 4, 2014 -
4:30 pm to 5:30 pm
Location: Cupples I, Room 199 |
Host: Peter Luthy
Abstract: Symplectic geometry a field of mathematics concerned with the study of a smooth manifold paired with a closed non-degenerate 2-form. The original motivation for studying such manifolds arose in physics, specifically in Hamiltonian mechanics in which the phase space of a system naturally has the structure of a symplectic manifold. An integrable system is a 2n dimensional symplectic manifold paired with n independent functions which Poisson commute. Such systems have a particularly nice structure and are of interest to a variety of people. In this talk we will introduce symplectic geometry for the complete beginner, learn enough to define and understand basic integrable systems, and time permitting we will talk about the more complicated properties of these systems, such as action-angle coordinates.
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