Math Science Literature Lecture Series
Simon Donaldson - Stony Brook University
Abstract: In 1978 (Physics Letters 65A) Atiyah, Hitchin, Drinfeld and Manin (ADHM) described a construction of the general solution of the Yang-Mills instanton equations over the 4-sphere using linear algebra. This was a major landmark in the modern interaction between geometry and physics, and the construction has been the scene for much research activity up to the present day. In this lecture we will review the background and the original ADHM proof, using Penrose’s twistor theory and results on algebraic vector bundles over projective 3-space. As time permits, we will also discuss some further developments, for example the work of Nahm on monopoles and connections to Mukai duality for bundles over complex tori.
Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.”
The schedule will be updated as talks are confirmed.