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MATHEMATICAL ASPECTS OF THE PHYSICS WITH NON-SELF-ADJOINT OPERATORS: 10 YEARS AFTER MARSEILLE, MARCH 23 { 27, 2020 SCHEDULE AND ABSTRACTS Schedule Monday, 23rd March 08.15 - 08.30 Welcome & Opening 08.30 - 09.10 Beatrice Pelloni: The quantization of solution of linear evolution PDEs 09.15 - 09.40 Lucrezia Cossetti: Absence of eigenvalues of Schr¨odinger,Dirac and Pauli Hamiltonians via the method of multipliers 09.45 - 10.10 Frantiˇsek Stampach:ˇ On Lieb-Thirring inequlities for non-self-adjoint Jacobi matrices 10.10 - 10.40 Coffee Break 10.40 - 11.20 Filippo Gazzola: Long-time Dynamics of An Extensible Hinged-Free Plate 11.25 - 11.50 Sabine B¨ogli: Essential numerical ranges for linear operator pencils 11.55 - 12.20 Borbala Gerhat: Schur complement dominant operator matrices 12.30 - 14.30 Lunch 14.30 - 15.10 Ross Pinsky: Markov Search Problems for a Stationary Target 15.15 - 15.40 Uwe G¨unther: Asymptotic spectral scaling graphs for IR-truncated PT −symmetric model Hamiltonians with V = −(ix)2n+1 potentials and beyond 15.45 - 16.10 Sergiusz Kuzhel: Lax-Phillips Scattering Method in Studies of Non-self-adjoint Schr¨odingerOperators 16.10 - 16.40 Coffee Break 16.40 - 17:20 Nicolas Raymond: A first formula of pure magnetic tunnel effect 17.25 - 17.50 Cristian Cazacu: Weighted Hardy-Rellich type inequalities 17.55 - 18.20 Robin Lang: On the eigenvalues of the Robin Laplacian with a complex parameter 18.25 - 19.30 Poster Exhibition 19.30 Dinner Date: March 4, 2020. Tuesday, 24th March 08.30 - 09.10 Alain Joye: Nonlinear Quantum Adiabatic Approximation 09.15 - 09.40 Fr´ed´ericH´erau: Non-selfadjoint tools in kinetic theory 09.45 - 10.10 Martin Vogel: Almost sure Weyl asymptotics for nonselfadjoint Toeplitz operators 10.10 - 10.40 Coffee Break 10.40 - 11.20 Guy Bouchitt´e: A repulsive multi-marginal transport model in quantum chemistry 11.25 - 11.50 Iveta Semor´adov´a: Spectral approximation of Schr¨odingeroperators with complex poten- tials: diverging eigenvalues 11.55 - 12.20 Juan Manuel P´erezPardo: Quantum controllability of infinite dimensional quantum systems based on Quantum Graphs 12.30 - 13.45 Lunch 13.45 - 13.50 COST Action presentation COST Invited Talk 13.55 - 14.35 Amru Hussein: Non-self-adjoint graphs: spectra, similarity, semigroups COST Session I 14.40 - 15.05 MatˇejTuˇsek: Location of hot spots in thin curved strips 15.10 - 15.35 Michal Tich´y: Large-time behaviour of the heat equation in sheared strips 15.40 - 16.05 Biagio Cassano: Location of eigenvalues of non-self-adjoint discrete Dirac operators 16.10 - 16:35 Tereza Kurimaiov´a: When damping cannot be detected from spectral data 16.35 - 17.05 Coffee Break 17.05 - 17:45 Michael Ruzhansky: Nonharmonic analysis of boundary value problems 17.50 - 18.50 Open Problem Session 19.30 Dinner Wednesday, 25th March 08.30 - 09.10 Tanya Christiansen: Asymptotic location of resonances for Schr¨odingeroperators on in- finite cylinders 09.15 - 09.40 Yaniv Almog: On the stability of laminar flows between plates 09.45 - 10.10 Sergey Tumanov: Completeness theorem for the system of eigenfunctions of the complex 2 2 2=3 Schr¨odingeroperator Lc = −d =dx + cx 10.10 - 10.40 Coffee Break 10.40 - 11.20 Albrecht B¨ottcher: Lattices from equiangular tight frames 11.25 - 11.50 Frank R¨osler: On The Solvability Complexity Index for Unbounded Selfadjoint Operators and Schr¨odingerOperators 11.55 - 12.20 Duc Tho Nguyen Classical and semi-classical analysis of magnetic fields in two dimensions 12.30 - 14.30 Lunch 14.30 - 19:00 Free Afternoon 19.30 Dinner Thursday, 26th March 08.30 - 09.10 Ari Laptev: Symmetry Results in Two-Dimensional Inequalitiesfor AharonovBohm Mag- netic Fields 09.15 - 09.40 Yehuda Pinchover: How large can Hardy-weight be? 09.45 - 10.10 Idan Versano: On families of optimal Hardy-weights for linear second order elliptic oper- ators 10.10 - 10.40 Coffee Break 10.40 - 11.20 Mariana Haragus: Linear stability of spectrally stable Lugiato-Lefever periodic waves 11.25 - 11.50 Catherine Drysdale: Complications regarding Amplitude Equations for Non-self-adjoint Operators 11.55 - 12.20 Tobias Bolle: Selectively non-self-adjoint linear fluid dynamics 12.30 - 14.15 Lunch COST Session II 14.15 - 14.40 Marjeta Kramar Fijavˇz: Linear Hyperbolic Systems on Networks 14.45 - 15.10 Luka Grubiˇsi´c: Contour integration methods fro sectorial operators 15.15 - 15.40 Ivica Naki´c: Uncertainty relations for second order elliptic operators 15.45 - 16.10 Jean-Bernard Bru: LiebRobinson Bounds for MultiCommutators 16.10 - 16.40 Coffee Break 16.40 - 17:20 Denis Grebenkov: The Bloch-Torrey operator: eigenmodes localization, branching spec- trum, asymptotic analysis, and applications 17.25 - 18.25 Open Problem Session 19.30 Conference Dinner Friday, 27th March 08.30 - 09.10 Charles Batty: Rates of decay of energy via operator semigroups and tauberian theorems 09.15 - 09.40 Tom Ter Elst: The Dirichlet problem without the maximum principle 09.45 - 10.10 Valentin Zagrebnov Trotter product formula for non-self-adjoint Gibbs semigroups 10.10 - 10.40 Coffee Break 10.40 - 11.20 Sonia Fliss: Scattering problem in general waveguides 11.25 - 11.50 Kirankumar Hiremath: Non-self-adjoint eigenvalue problem of optical bent waveguides 11.55 - 12.20 Archit Kulkarni: Gaussian Regularization of the Pseudospectrum and Davies' Conjecture 12.30 - 14.30 Lunch 14.30 - 15.10 Nicolas Burq: Observability for Schr¨odingerGrushin operators 15.15 - 15.40 Irfan Glogi´c: Spectral properties of the wave operator in self-similar coordinates 15.45 - 16.10 Vladimir Lotoreichik: Optimization of lowest Robin eigenvalues on 2-manifolds and un- bounded cones 16.10 - 16.40 Coffee Break 19.30 Dinner 1. Invited talks 1. Charles Batty Title: Rates of decay of energy via operator semigroups and tauberian theorems Abstract: An approach to studying decay of energy of damped waves and similar models involves considering a non-self-adjoint operator which generates an operator semigroup, and finding or estimating the norm of its resolvent on the imaginary axis. I will describe how the rate of decay can then be determined by applying recent results of tauberian type about operator semigroups. 2. Albrecht B¨ottcher Title: Lattices from equiangular tight frames Abstract: I take the liberty to leave the field of genuine operator theory and to move into linear algebra and (non-self-adjoint) matrix theory. The talk is about the question when certain matrices do generate a lattice, that is, a discrete subgroup of some finite-dimensional Euclidean space, and if this happens, which good properties these lattice have. The matrices considered come from equiangular tight frames. I promise a nice tour through some basics of equiangular lines, tight frames, and lattice theory. We will encounter lots of interesting vectors and matrices and enjoy some true treats in the intersection of discrete mathematics and finite-dimensional operator theory. 3. Guy Bouchitt´e Title: A repulsive multi-marginal transport model in quantum chemistry Abstract: An interesting issue in Density Functional Theory (DFT), an important branch of Quantum Chemistry, is to understand the asymptotic behavior as " ! 0 of the infimum problem d min "T (ρ) + C(ρ) − U(ρ): ρ 2 PR where " is a small parameter which depends on the Planck constant and - T (ρ) is the kinetic energy Z p T (ρ) = jr ρj2 dx; d R - C(ρ) describes the electron-electron interaction; - U(ρ) is the potential term Z U(ρ) = V (x)ρ dx; d R - P is the class of all probabilities over Rd. In this talk we propose a duality approach for the N-marginal repulsive cost C(ρ) which involves continuous functions vanishing at infinity and allows to consider minimizers ρ which are sub-probabilities (ionization). Then we give primal-dual necessary and sufficient optimality conditions for an optimal pair (ρ, ') with • ' an Kantorovich potential for ρ (Optimal transport) p • u = ρ a ground state for −"∆ + (' − V ). In a last part of the talk, we apply our results to the asymptotic as " ! 0 and, in some cases, we give evidence of a mass quantization effect for optimal sub-probabilities. This is a joined work with G. Buttazzo (Pisa), T.Champion (Toulon), L. De Pascale (Firenze). 4. Nicolas Burq Title: Observability for Schr¨odingerGrushin operators Abstract: This talk I will present some recent results on the two dimensional Grushin Schr¨odinger equation posed on a finite cylinder Ω = (−1; 1)x × Ty with Dirichlet boundary condition. We obtain the sharp observability by any horizontal strip, with the optimal time T∗ > 0 depending on the size of the strip. Consequently, we prove the exact controllability for Grushin Schr¨odinger equation. By exploiting the concentration of eigenfunctions of harmonic oscillator at x = 0, we also show that the observability fails for any T ≤ T∗. This is a joint work with Chenmin Sun (Cergy). 5. Tanya Christiansen Title: Asymptotic location of resonances for Schr¨odingeroperators on infinite cylinders Abstract: We consider Schr¨odingeroperators on the particular infinite cylinder X = R × S1, with bounded, compactly supported potential V . We show that in the high energy limit, reso- nances which lie \near" the physical sheet are close to points determined by the resonances of a Schr¨odingeroperator on the line, and discuss some refinements and applications. 6. Sonia Fliss Title: Scattering problem in general waveguides Abstract: We consider in this talk various time harmonic wave problems in infinite waveguides. The study of such problem present theoretical and numerical difficulties. From a theoretical point of view, one has to determine a radiation condition which characterizes the behaviour of the scattered waves at infinity, and which is essential to obtain well-posedness of the scattering problem.
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