Topology & Equivariant Theories 
A1, A2, A3, A5, A6, A7

Dynamics & Variational Methods 
B1, B2, B3, B4, B5, B6, B7

Algebra, Combinatorics & Optimization 
C1, C2, C3, C4, C5

MercatorFellow 
20172020


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, RiemannHilbert 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, CalogeroMoser systems in dimension two, and, on the partial differential equations side, soliton and breather asymptotics for the cubic nonlinear Schrödinger equation, which can also include a δpotential on the righthand side (destroying the complete integrability)  Group:  
 Prof. Igor Burban (PI)  mail: burban at math.unipaderborn.de  phone: 05251 / 60 2619  room: D2 213  Institute of Mathematics  Paderborn University 
  Prof. Markus Kunze (PI)  mail: mkunze at math.unikoeln.de  phone: 0221 / 470 7075  room: 129  Mathematical Institute  University of Cologne 
  Kevin Gruner, M.Sc. (ds)  mail: kgruner at math.unikoeln.de  phone: 0221 / 470 7453  room: 120  Mathematical Institute  University of Cologne 
  Yana Staneva, M.Sc. (ds)  mail: ystaneva at math.unikoeln.de  phone: 49 (0)221 / 470 1740  room: 121  Mathematical Institute  University of Cologne 


