Dept Math & Stat UiT, Forskningsparken B459
  Lecture series joint with Zoom seminar GRIEG: 27.04, 11.05, 25.05 2021 Tue 15:00-16:00

Boris Kruglikov (UiT)

Dispersionless integrable systems

In this three-lecture course I will introduce the audience to the techniques of infinite-dimensional integrable systems. I will start with soliton equations and recall the integrability approaches. Then I will discuss the dispersionless limit and the traces of the integrability. Then I will concentrate on dispersionless systems and relate their integrability to geometry. This is based on hydrodynamic methods, formal theory of differential equations and twistor theory. We will concentrate on nondegenerate PDEs, and (somewhat unexpectedly) this implies that the number of independent variables cannot exceed 4. The most interesting cases are dimensions three and four, when the geometry behind the integrability will be shown to be a specification of the conformal geometry, namely Einstein-Weyl in 3D and Self-Duality in 4D. The corresponding equations are therefore the master equations of the theory. Several examples will be discussed.

Lectures series is hybrid: in person and via Zoom (to get the link, please contact Boris Kruglikov).