Geometry working seminar

Wednesday, May 23, 2012 — 1:00 PM to 4:00 PM EDT

Li Chen

“Symmetry groups of differential equations, Part I.”

Abstract:
The goal of this talk is to present a way of discovering symmetries hidden inside systems of differential equations. First, I will present a survey of some basic Lie group theory. Then we will consider actions of Lie groups on solutions of differential equations and will pay special attention to the ones that leaves the solutions invariant. I will also introduce the concept of the prolongation of a Lie group action and use it to formulate symmetry groups of differential equations. In the course the of the talk, I will also supply concrete examples of how the theory works. This will be the first of two parts.

Ruxandra Moraru

will speak on

“Metric connections I: the Levi-Civita connection”

Abstract
This is the first in a series of lectures on metric connections. On a smooth vector bundle, a connection provides a way of computing covariant derivatives of smooth sections of the bundle or of metrics on the bundle. If one fixes a metric and the covariant derivatives of the metric vanish with respect to a given connection, then this connection is said to be (compatible with the) metric. In this talk, I will begin by introducing connections on smooth vector bundles and present some of their properties. I will then specialize to affine connections on the tangent bundle, in particular giving a geometric interpretation of the curvature and the torsion of an affine connection. I will finally discuss the Levi-Civita connection on a Riemannian manifold, which is the unique torsion-free connection that is compatible with the Riemannian metric. Although I will briefly recall the notion of vector bundle, I will assume the knowledge of differential forms.

Location

200 University Avenue West
Waterloo, ON N2L 3G1
Canada