The fourth visit of Sir Michael Atiyah as IAS Visiting Member explores the nucleus model from various aspects, including the skyrmions, the Seiberg-Witten equations and his own speculations based on various ideas.
Professor Atiyah has made fundamental contributions to many areas of mathematics, in particular on topology, geometry and analysis. From his first major contribution - topological K-theory - to his more recent work on quantum field theory, Professor Atiyah has been influential in the development of new theoretical tools and has supplied far-reaching insights. He is a notable collaborator, with his name linked with other outstanding mathematicians through their joint research. Professor Atiyah has been the recipient of many honors and awards, including the Fields Medal in 1966 and the Abel Prize in 2004. He was knighted in 1983 and made a member of the Order of Merit in 1992.
Abstract
1.The Skyrme model of the nucleus
About 75 years ago Tony Skyrme proposed a non-linear model for the classical proton/neutron. In modern parlance these "skyrmions" are solitons and they have considerable mathematical and physical interest. I will survey the history and current activity in the field, which is mainly due to Nick Manton and his collaborators.
2. The Seiberg-Witten equations
In the 1980's Simon Donaldson revolutionized our understanding of 4-dimensional manifolds by using solitons of Yang-Mills theory. A decade later Seiberg and Witten introduced their equations which turn out to produce a theory essentially equivalent (or dual) to Donaldson theory. These provide additional insight and I will review this material.
3. A new speculative model for the nucleus
In this lecture I will explore some new speculative ideas for a more comprehensive model for the nucleus, which builds on the ideas of Skyrme and of Seiberg-Witten. 4-dimensional manifolds, particularly complex algebraic surfaces will play a key role.
