08 Sep 2009; Mat-Nat Faculty (UiTø), room U7=A152. Tuesday 12:15-14:00.

Boris Kruglikov

"Integration of class N=1 PDE systems".

Class N=1 systems were considered by Sophus Lie in 1893. Informally these are overdetermined scalar systems of PDEs on the plane with functional freedom of solution being 1 function of 1 variable. Lie's theorem claims that such systems are integrable via ODE methods. I will demonstrate this by relating N=1 systems to rank 2 distributions. Then I'll describe the  geometry of rank 2 distributions vs. the integrability of PDEs. Finally I will talk on most symmetric models of these objects.