Abstract

SPEAKER:	Professor John D. McCarthy - Michigan State University
TITLE:	A Different Kind of Geometry
ABSTRACT:	Symplectic geometry, the study of symplectic manifolds, is a different kind of geometry which originated as a mathematical outgrowth of Hamiltonian mechanics. This subject has been one of the most rapidly advancing areas of mathematics over the past ten years. In this talk, we shall introduce the notion of a symplectic manifold via the concepts of undergraduate vector calculus (e.g. tangent vectors, directional derivatives), explain how such manifolds arise as spaces occuring in Hamiltonian mechanics, and discuss how one is able to construct other examples of such manifolds (e.g. four-dimensional symplectic manifolds).