Mark Green Hodge Theory and Boundary Components of Moduli of Surfaces

Robert Bryant From Mechanics, to Algebra, to Geometry: The Notion of Holonomy. Abstract: Familiar mechanical phenomena, 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, came 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.” This talk will discuss some holonomic phenomena in everyday life, explore their underlying commonality, their appearance in more advanced situations, and try to provide some insight into why this idea has turned out to be so fundamental.