Andrii Liashyk , Nicolai Reshetikhin , Ruijie Xu

Hank Chen

Monday, September 14, 2026 3:30 PM - 4:30 PM

A7-201

It is well-known that the structure of Poisson-Lie groups and Lie bialgebras play a major role in the study of 1+1d integrable systems; indeed, their Lax pairs can often be constructed from a classical r-matrix and its associated Lie bialgebra. Higher homotopical and derived versions of these ideas have also been recently studied -- these came under the name of "Poisson-Lie 2-groups, Lie 2-bialgebras and the classical 2-r-matrices". In this talk, I will explain how one can use such differential-graded (dg) structures to probe higher-dimensional notions of Lax integrability. In particular, I will highlight how we can construct derived Lax pairs canonically from the dg Kostant-Kirilov r-bracket. Moreover, we show how the framework of a Kac-Moody dg algebra allows the dg Lax equations to be rewritten as a zero 2-curvature condition. As an example, I will explicitly demonstrate the dg Lax integrability of a 3d sigma model.