## Open problems in non-self-adjoint spectral theory

 suggested by the participants of the conference series Mathematical aspects of the physics with non-self-adjoint operators and related meetings. Some of the open problems have been published in the journal Integral Equations and Operator Theory (Birkhauser).

## 2013 ICMS meeting

 2013-01-ICMS: published version updates Spectral theory of Sturm-Liouville operators with indefinite weights by J. Behrndt Behrndt, J.: Integr. Equ. Oper. Theory (2013) 77: 299. Levitin, M and Seri, M: Oper. Matrices 10 (2016), 223-245. 2013-02-ICMS: Magnetic resonances and meromorphic families of non-self-adjoint operators by V. Bruneau 2013-03-ICMS: A Riemann-Hilbert approach to Toeplitz operators and the corona theorem by C. Camara 2013-04-ICMS: Stability of regularized shock solutions in coating flows by M. Chugunova 2013-05-ICMS: 1D Dirac operators with trigonometric polynomial potentials by P. Djakov 2013-06-ICMS: The spectrum of second order multi-point problems by F. Genoud presentation 2013-07-ICMS: The complex cubic oscillator: spectral instability and real spectrum by R. Henry 2013-08-ICMS: Perturbation determinant and the Evans function by I. Karambal presentation 2013-09-ICMS: Differential operators with exotic boundary conditions arising in probability theory by M. Kolb 2013-10-ICMS: The cloaking effect in metamaterials: beyond ellipticity by D. Krejcirik 2013-11-ICMS: Computing spectral determinants for multi-dimensional non-selfadjoint operators by S. Malham 2013-12-ICMS: Alternative proofs of maximal and non maximal subelliptic estimates for geometric Kramers-Fokker-Planck equations by F. Nier 2013-13-ICMS: Two open problems from linear stability analysis in hydrodynamics by C. Tretter presentation 2013-14-ICMS: The rate of exponential resolvent growth for quadratic operators by J. Viola presentation 2013-15-ICMS: Eigenvalue statistics for a model non-self-adjoint semiclassical differential operator with a small random perturbation by M. Vogel presentation 2013-16-ICMS: Real resonances of Schroedinger operators with complex-valued potentials by X. P. Wang presentation

## 2012 OTAMP meeting

 2012-01-OTAMP: Basis properties of the eigenvectors of a PT-symmetric Sturm-Liouville operator by L. Boulton 2012-02-OTAMP: Curved Dirichlet waveguides in strong magnetic field by P. Exner 2012-03-OTAMP: Large-time behaviour of the heat equation: subcriticality versus criticality by D. Krejcirik 2012-04-OTAMP: "Strange" functions in the Laplace operator domains and their relation to the eigenfunctions by J. Kriz 2012-05-OTAMP: Asymptotics of solution of a certain ODE by A. Luger 2012-06-OTAMP: On the invertibility of convolution operators on cones by H. Mascarenhas 2012-07-OTAMP: Self-adjoint Jacobi operators possessing generalized eigenvectors with the strongly increasing phase sequence: do they exist? by M. Moszynski

## 2010 ESF meeting

 2010-01-ESF: published version updates Open problems regarding applying non-self-adjoint operator techniques to the p-Laplace non-linear operator in one dimension by L. Boulton Boulton, L.: Integr. Equ. Oper. Theory (2012) 74: 1. Edmunds, D. E. , Gurka, P. and Lang, J.: Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 470 (2014), 20140221. 2010-02-ESF: The Weyl law for resonances of operators with variable coefficients on graphs by E. B. Davies 2010-03-ESF: published version Decay law regularity by P. Exner Exner, P.: Integr. Equ. Oper. Theory (2012) 72: 1. 2010-04-ESF: published version Complex symmetric operators by S. R. Garcia Garcia, S.R.: Integr. Equ. Oper. Theory (2012) 72: 3. 2010-05-ESF: The de Sitter group representations: open questions by J.-P. Gazeau 2010-06-ESF: published version The spectrum of the Hilbert matrix as an operator on $\ell_p$ by M. Gonzalez Gonzalez, M.: Integr. Equ. Oper. Theory (2012) 74: 3. 2010-07-ESF: published version PT-symmetric waveguides and the lack of variational techniques by D. Krejcirik Krejcirik, D.: Integr. Equ. Oper. Theory (2012) 73: 1. 2010-08-ESF: The large-time behaviour of the heat kernel: subcriticality versus criticality by D. Krejcirik 2010-09-ESF: published version The growth order of a solution of a non-self-adjoint differential equation by M. Marletta Marletta, M.: Integr. Equ. Oper. Theory (2012) 72: 5. 2010-10-ESF: published version PT-symmetric Laplace-Beltrami operator in the strip on a sphere by P. Siegl Siegl, P.: Integr. Equ. Oper. Theory (2012) 73: 5. 2010-11-ESF: Some open problems related to the Weyl asymptotics for non-self-adjoint operators by J. Sjostrand 2010-12-ESF: published version Uniform time-decay of semigroups of contractions by X. P. Wang Wang, X.P.: Integr. Equ. Oper. Theory (2012) 73: 3. 2010-13-ESF: published version Matrix Hamiltonians with a chance of being complex symmetric by M. Znojil Znojil, M.: Integr. Equ. Oper. Theory (2012) 74: 5. 2010-14-ESF: Open problem in non-selfadjoint linear second-order ODE's in complex domain: the proof of the reality of spectra for quantum toboggans by M. Znojil

## Other

 2012-01-OTHER: published version Lieb-Thirring Type Inequalities for Schroedinger Operators with a Complex-Valued Potential by M. Demuth and M. Hansmann and G. Katriel Demuth, M., Hansmann, M. and Katriel, G.: Integr. Equ. Oper. Theory (2013) 75: 1. 2012-02-OTHER: published version Combinatorial Identities Related to Eigen-Function Decompositions of Hill operators: Open Questions by P. Djakov and B. Mityagin Djakov, P. and Mityagin, B.: Integr. Equ. Oper. Theory (2013) 75: 7.

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