Integrable Systems (and Infinite Dimensional Lie Algebras)
SS 2021 •
Prof Dr Christoph Bohle
Assistent: Jonas Ziefle
Integrable systems are differential or difference equations with
extraordinarily large symmetry group. The course will focus on
equations related to the Korteweg de Vries (KdV) equation and discrete
counterparts. Originally a mathematical model for the soliton
phenomenon discovered during a famous horse ride along a canal,
equations of KdV type have now many applications and the underlying
theory involves various mathematical disciplines.
A fundamental idea for understanding and solving KdV type equations is
their interpretation as spectrum preserving deformations of underlying
auxiliary linear operators - in the simplest case symmetric matrices.
This lecture is the continuation of the lecture called "Introduction to
Integrable Systems (Classical Mechanics, Riemann Surfaces, and Spectral
Theory)". This continuation will investigate integrable equations using
sl(2,C)--loop algebras. In particular, we will study explcit solutions
that can be described using the theory of hyperelliptic Riemann surfaces.
(Prerequisites: Basic knowledge of the material presented in Part I of the lecture called
"Introduction to Integrable Systems (Classical Mechanics, Riemann Surfaces, and Spectral Theory)")
The lectures will be held online - in the same format as last semester. The exercise sessions in a hybrid format (partially online and - if possible - partially at the institute). Schedule for synchronous part:
| Lecture | | Tue.+Thu. 12.30-13.30 | | online |
| Excercise | |
? | | ? +online. |
Everything will be recorded.
Further information as well as the course material and links to the lectures can be found in
(The password of last semester remains valid. If you are a new participant or don't have the password anymore, please contact
who will send you the moodle password.)