Symplectic Structures in Geometry, Algebra and Dynamics
Collaborative Research Centre TRR 191
 
A1, A2, A3, A5, A6, A7
B1, B2, B3, B4, B5, B6, B7
C1, C2, C3, C4, C5
Dynamics & Variational Methods
B6: Algebraic and analytic aspects of integrable systems
Burban, Kunze
Abstract:
The aim of this project is to study completely integrable dynamical systems in finite and infinite dimensions, using techniques from algebraic geometry, homological algebra, Riemann-Hilbert problems and soliton dynamics. The common feature of all those problems is that algebraic or dynamic information can be derived from the knowledge of certain ‘spectral objects’. More specifically, we shall address the Krichever correspondence for ordinary and partial differential operators, Calogero-Moser systems in dimension two, and, on the partial differential equations side, soliton and breather asymptotics for the cubic non-linear Schrödinger equation, which can also include a δ-potential on the right-hand side (destroying the complete integrability)
Group:
 
Prof. Igor Burban (PI)
mail: burban at math.uni-koeln.de
phone: 0221 / 470 3431
room: 106
Mathematical Institute
University of Cologne
Prof. Markus Kunze (PI)
mail: mkunze at math.uni-koeln.de
phone: 0221 / 470 7075
room: 129
Mathematical Institute
University of Cologne
Aaron Saalmann (ds)
mail: asaalmann at math.uni-koeln.de
phone: 0221 / 470 7453
room: 120
Mathematical Institute
University of Cologne
Impressum Institution of DFG, MI University of Cologne and FM Ruhr-University Bochum