Spectral Analysis, Stability and Bifurcation in Modern Nonlinear Physical Systems (12w5073)
Paul Binding (University of Calgary)
Thomas Bridges (University of Surrey)
Yasuhide Fukumoto (Kyushu University)
Igor Hoveijn (Noordelijke Hogeschool Leeuwarden)
Oleg Kirillov (Helmholtz-Zentrum Dresden-Rossendorf)
Dmitry Pelinovsky (McMaster University)
The aim of the meeting is to bring together people from different disciplines each studying these stability questions from their own perspectives, rooted in established traditions. Recent mathematical and physical facts point out the existence of hidden new intriguing connections between the original researches of the invitees. We feel that an atmosphere of co-education and co-discovery of the BIRS workshop will help us to clarify the existing analogies, stimulate active cross-usage of methods and approaches that finally will result in establishing new links connecting different mathematical disciplines and seemingly different applications. One of the central aims is to give a deeper and broader understanding to all participants of stability questions and to unify various methods and treatments which may in turn lead to the birth of new directions of investigation.
It is expected that participants of the workshop will establish spontaneous contacts with each other according to their tastes and interests. However, selection of some critical directions of research seems to be necessary to focus the efforts. Ideally, the research topics should be formulated in such a manner that both applied and pure scientist feel comfortable because of definite mutual interest. Taking this into account we think that the possible focus groups will be:
1) Instability index, Maslov index (geometry, topology etc), geometrical phase, geometrical optics
2) Instabilities in PDEs from elasticity, fluids, magnetohydrodynamics, fluid-structure interactions etc.
3) Perturbation and asymptotic analysis of multiparameter eigenvalue problems (eigencurves, singularities of different surfaces related to stability)
4) Hamiltonian and reversible systems, dissipation-induced instabilities (development of a general theory and interpretations for applications)
5) Numerical analysis, applied linear algebra (computational aspects related to tracking the eigenvalues and eigenvectors, parallel transport of eigenvectors, computation of indices, finding multiple eigenvalues of non-Hermitian operators, pseudospectra)
6) Symmetries and stability (equivariance, fundamental symmetry, influence of symmetries hidden in the boundary conditions)