title: "The Gauge/Bethe Correspondence Revisited via Quiver BPS Algebras"

abstract: The celebrated Gauge/Bethe correspondence claims the correspondence between the vacuum equations of supersymmetric field theories with four supercharges on the one hand, and the Bethe ansatz equations of associated quantum integrable models, on the other. This correspondence has been studied intensively both in physics and mathematics, and hundreds of papers have been written on the subject. It is, however, not clear yet how general the Gauge/Bethe correspondence should be---at least this has been my opinion for many years. In this lecture I will revisit this decade-old question, based on recent developments in quiver BPS algebrals (see Dimitry Galakhov, Wei Li, Masahito Yamazaki; arXiv:2206.13340 [hep-th] and earlier works). Since I heard some people in Beijing have been interested in this topic, I am hoping to discuss a bit more technical details than a typical talk.