Differential Geometry for Engineers
Friday 22 June 2018
Ballroom H
Overview
This tutorial endeavours to introduce differential geometry simply, efficiently, rigorously and engagingly. A motivating example used throughout is optimisation on manifolds: how can gradient descent or a Newton method be performed on a manifold? An integral part of the tutorial is teaching how to do calculations involving manifolds, including how to compute derivatives, tangent spaces, curvature and so forth. At a higher level, the different ways of working with manifolds will be explained (e.g., extrinsic coordinates versus local coordinates), and ways for extending algorithms from Euclidean space to manifolds will be discussed.
Schedule
8:30-9:15 Motivation and Multi-dimensional Differential Calculus
9:15-10:00 Tangent Spaces and Directional Derivatives
10:00-10:30 Coffee Break
10:30-11:15 Concrete Manifolds, Coordinate Charts and Smooth Functions
11:15-12:00 Metrics, Parallel Transport and Connections
12:00-12:30 Gradients, Hessians and Worked Examples
Presenter
Jonathan Manton, University of Melbourne