# The idea of holonomy. Fifty-First Annual DeLong Lectures. University of Colorado at Boulder. October 13, 2014

Invited Talk

The notion of 'holonomy' in mechanical systems has been around for more than a century and gives insight into daily operations as mundane as steering and parallel parking and in understanding the behavior of balls (or more general objects) rolling on a surface with friction. A sample question is this: What is the best way to roll a ball over a flat surface, without twisting or slipping, so that it arrives at at given point with a given orientation? In geometry and physics, holonomy has turned up in many surprising ways and continues to be explored as a fundamental invariant of geometric structures. In this talk, I will illustrate the fundamental ideas in the theory of holonomy using familiar physical objects and explain how it is also related to group theory and symmetries of basic geometric objects.

### Service Performed By

- Bryant, Robert Phillip Griffiths Professor of Mathematics

### Date

- October 13, 2014

### Service or Event Name

- Fifty-First Annual DeLong Lectures

### Host Organization

- University of Colorado at Boulder

### Location or Venue

- University of Colorado at Boulder