RTGC Seminar: Integrable dispersionless systems via the geometry of solutions and the solutions spaces.

Seminar | March 10 | 4-5:30 p.m. | 939 Evans Hall

 Boris Kruglikov, University of Tromso

 Department of Mathematics

Recently, in a series of joint works with E.Ferapontov (Loughborough), M.Dunajski (Cambridge), D.Calderbank (Bath) and others, we studied relations between integrable (via Lax pair) dispersionless equations in 3D and 4D and the differential geometry on their solutions. This allows to rigorously demonstrate that Einstein-Weyl equations in 3D and self-duality equations in 4D are master-equations for dispersionless integrable systems, as predicted by twistor theory. Thus dispersionless integrable systems have functional parameters and are more plentiful than the solitonic integrable equations (to which dispersionless ones serve as a limiting set). I will also describe the moduli in some particular classes of integrable equations. In those cases integrability can be also visualised via the geometry of the solution spaces. In higher dimensions dispersionless equations arise in hierarchies, and the corresponding geometry is more complicated (generalised conformal geometry, GL2-geometry, etc).