Scientific programme

The workshop is aiming at mathematical studies of non-self-adjoint problems coming from modern physics with a special emphasis put on rigorous justifications of phenomena encountered in the newly developing fields represented by PT-symmetric quantum mechanics and quantization in the de Sitter spacetime. The non-self-adjoint theory is extremely diverse, it comprises a collection of advanced methods and it is difficult, if not impossible, to find a common thread. We plan to gather scientists encountering the non-self-adjoint operators in various contexts, with different goals and techniques, and who would not ordinarily participate in the same research group.

Among other topics covered, the workshop is intended to be particularly concerned with:
  • PT-symmetric quantum mechanics
  • quantization in the de Sitter spacetime
  • non-self-adjoint perturbation theory
  • quantitative bounds on operators, pseudospectra
  • complex symmetric operators
  • Krein spaces
  • damped wave systems

Talks

T. Azizov Operators of the class K(H) and PT symmetric operators
H. Bergeron Coherent states based on non-self-adjoint operators: From the harmonic oscillator to any one dimensional Hamiltonian
G. Bouchitte Transmission between media with opposite sign dielectric constants and anomalous resonances
L. Boulton A non-orthogonal spectral method in one dimension
H. Cornean On the transfer matrix of a MIMO system
E. B. Davies Resonances of quantum graphs
S. Garcia Complex symmetric operators: an overiew
J.-P. Gazeau The de Sitter group representations: old results and new questions
A. Laptev Eigenvalue estimates for Schrodinger operators with complex potentials
U. Moschella Scalar tachyons in the de Sitter Universe
H. Neidhardt On perturbation determinants for non-selfadjoint operators
P. Siegl Open problems in PT-symmetry
J. Sjostrand Distribution of eigenvalues of non-self-adjoint differential operators and spectral instability
K. Veselic How reliable is non-selfadjoint spectrum?
X. P. Wang High frequency analysis of the dissipative Helmholtz equation
M. Znojil PT-symmetric Hamiltonians: Non-self-adjoint or self-adjoint?
E. Zuazua Dissipative wave equations: asymptotic behavior and numerics

In addition to these scheduled talks, the participants are encouraged to report on open problems in discussion sessions.


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