Bhaumik Lecture: “Integrability and Four-Dimensional Gauge Theory”

Integrability and Four-Dimensional Gauge Theory” by Edward Witten

Some years ago, Kevin Costello introduced a new approach to the Yang-Baxter equation and integrable systems based on an unusual gauge theory in four dimensions.   The gauge theory in question is a close cousin of three-dimensional Chern-Simons theory, which almost thirty years ago was related to knot invariants and three-manifold invariants and has had a variety of physical applications.   The Yang-Baxter equation has a conspicuous analogy with knot theory, but prior to Costello’s work, it was unclear how the gauge theory/knot theory connection could be extended to the Yang-Baxter equation and integrability.  The talk will be an introduction to Costello’s approach, drawing also on recent work by Costello, Masahito Yamazaki, and the speaker.