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Dresden Memorial Lecture
Start Date: 4/24/2017Start Time: 4:15 PM
End Date: 4/24/2017End Time: 5:30 PM

Event Description:
The Department of Mathematics and Statistics of Swarthmore College invites all to The Dresden Memorial Lectures 2017.

Robert Bryant Duke
University

Time: 4:15 Refreshments Lecture: 4:30-5:30pm Monday April 24
Title: The Idea of Holonomy

Abstract: 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 property 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.

Tuesday April 25 Title: On the Geometry of Geodesics on Finsler Surfaces
Abstract: In recent years, our understanding of how the geometry of 'geodesics' (shortest curves joining two points) generalizes from the familiar case of surfaces in space to a wider class of geometries has improved greatly. After giving a brief introduction to Finsler surfaces to familiarize the audience, I'll report on some of these developments and some surprising examples and relations between them. Emphasis will be on the geometry and the motivations rather than computations, but I hope to explain some very recent work I and my collaborators have done classifying the geodesic flow on Finsler surfaces of constant curvature. — Brief biography: Robert Bryant received his PhD in 1979 at the University of North Carolina at Chapel Hill, working in differential geometry with applications to the geometry of systems of partial differential equations.

Duke has served on the faculty at Rice University, the University of California at Berkeley, and Duke University, where he is currently the Phillip Griffiths Professor of Mathematics. He served as the Director of the Mathematical Sciences Research Institute during 2007–2013 and as the President of the American Mathematical Society during 2015–2017. He is a Fellow of the American Academy of Arts and Sciences and a member of the US National Academy of Sciences. Professor Bryant’s research interests center on exterior differential systems and the geometry of differential equations, especially their applications to differential geometry, minimal submanifolds, special holonomy, integrable systems, and mathematical physics. He proved the local existence of and analyzed the generality of metrics with exceptional holonomy, producing the first explicit examples.
Location Information:
*Swarthmore College  (View Map)
500 College Avenue
Swarthmore, PA 19081

*Swarthmore College - Science Center
Room: Science Center 101 - Chang Hou Hall
Contact Information:
Name: L. Chen
Phone: 690-4763
Email: lchen@swarthmore.edu
Robert Bryant
Open To
The Public

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