From Mechanics, to Algebra, to Geometry: The Notion of Holonomy. McKnight Zame Lecture in Mathematics. University of Miami. March 1, 2018
Familiar mechanical phenomenon, such as driving and parking a car, rolling a ball, and even the ability of falling cats to land on their feet (usually) are examples of an underlying mathematical concept that, in the 19th century, became to be known as `holonomy'. As it became better understood, mathematicians and physicists began to realize that holonomy underlay many disparate phenomena, from the everyday situations mentioned above to understanding the curvature of space in Einstein's theory of general relativity. Nowadays, holonomy lies at the heart of both deep mathematical objects and high-energy physical theories, such as string theory and the still-mysterious M-theory, on which many theoretical physicists would like to base a 'theory of everything.
In this talk, after discussing some holonomic phenomena in everyday life, I'll explore their underlying commonality and their appearance in more advanced situations and try to provide some insight into why this idea has turned out to be so fundamental.
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