**Robert Bryant, Mathematical Sciences Research Institute**

**Thursday, October 14, 2010**

**Abstract: **The notion of `holonomy' in mechanical systems has been around for over one hundred years 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, holonomy has turned up in many surprising ways in the last 100 years 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.

**Biography: **Robert Bryant is the Director of the Mathematical Sciences Research Institute of Berkeley, CA. A North Carolina native, he received his PhD in mathematics in 1979 at the University of North Carolina at Chapel Hill, working under Robert B. Gardner. After serving on the faculty at Rice University for seven years, he moved to Duke University in 1987, where he held the Juanita M. Kreps Chair in Mathematics until moving to the University of California at Berkeley in July 2007. He has held numerous visiting positions at universities and research institutes around the world. He visited MSRI during the 2001-02 academic year as a Clay Mathematics Visiting Professor and he was in residence at MSRI during the Fall 2003 term as a co-organizer of the program in Differential Geometry.

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