Preseminar for graduate students:
Jon Nimmo Introduction to quasi-determinants
Mahmood-ul Hassan: Some aspects of the noncommutative principal chiral model
Folkert Mueller-Hoissen: A class of "partially linearizable" PDEs on associative algebras
Lump solutions of the KP and the pseudodual chiral model hierarchy
Olaf Lechtenfeld: The non-commutative sine-Gordon model
N=4 mechanics, WDVV equations and roots
Location: Room ???, Department of Mathematics.
Titles and abstracts: T.B.A.
Title: A class of "partially linearizable" PDEs on associative algebras
In the framework of bidifferential graded algebras we consider a class of
nonlinear partial differential (or difference) equations (with dependent
variable in an associative and typically noncommutative algebra), for which a
method exists generating exact solutions from a certain linear system of
PDEs. Special examples within this class are the self-dual Yang-Mills
equation and the Kadomtsev-Petviashvili (KP) hierarchy (in an associative
algebra). All this is based on joint work with A. Dimakis.
Title: Lump solutions of the KP and the pseudodual chiral model hierarchy
As an application of results of my previous talk, in particular (ordinary and
anomalous) multi-lump solutions of the scalar KP-I hierarchy are recovered
(via matrix KP solutions) and corresponding solutions of the hierarchy of the
"pseudodual chiral model" in 2+1 dimensions ("pseudodual" to Ward's
integrable chiral model) are obtained. This is essentially based on
Dimakis and Mueller-Hoissen, arXiv:0706.1373, arXiv:0712.3689.
Updated 3rd April 2008