Solitons, Instantons, and Twistors

Many interesting classical field configurations such as monopoles, vortices, and instantons arise as self-reinforcing stable finite energy solutions which are extremisers of some naturally associated functional. Constructing these solutions often involves solving highly nonlinear PDE’s such as the (Anti) Self-Dual Yang-Mills equations which calls upon techniques from various areas such as twistor theory, integrability, and gauge theory.

 

This reading group will be based on the book “Solitons, Instantons, and Twistors” with the primary aims of developing an understanding of classical integrability, twistor methods and gauge theoretic solitons/instantons.