The conference will make an overview of the state of the art in a rapidly developing area of analysis concerned with application of the techniques of operator theory to the asymptotic analysis of parameter-dependent differential equations and boundary-value problems. From the physical point of view, the parameter normally represents a length-scale in the situation modelled by the equation: for example, a wavelength in wave propagation, or the inhomogeneity size in the theory of periodic composites. The theory of linear operators in a Hilbert space (symmetric, self-adjoint, dissipative, non-selfadjoint), which has enjoyed several decades of outstanding progress, had been, for much of its time, restricted to abstract analysis of general classes of operators, accompanied by ad-hoc examples and applications to perturbations of the Laplace operator. The meeting is aimed at making a step-change in re-assessing the existing body of knowledge in the related areas, as a modern operator-theoretic version of the classical asymptotic analysis. This will generate new research directions in the asymptotic study of operator families, where the abstract and applied streams are aligned with each other.
Confirmed speakers:
- Yves Capdeboscq (University of Oxford, UK) "Small volume asymptotics for Maxwell's equations"
- Giuseppe Cardone (University of Sannio, Italy) "Gaps in the spectrum of Neumann problems on waveguides with strongly corrugated boundary''
- Tanya Christiansen (University of Missouri, USA) "Sharp lower bounds on a resonance counting function in even-dimensional Euclidean scattering"
- Pavel Exner (Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Academy of Sciences) "Singular Schrödinger operators and Robin billiards: geometry, spectra and asymptotic expansions"
- Davit Haratyunyan (University of Utah, USA) "High-frequency homogenization for traveling waves in periodic media"
- Rostyslav Hryniv (University of Rzeszów, Poland, and Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine) "Schrödinger operators with δ'-like potentials"
- Ilia Kamotski (University College London, UK)
- Alexander Kiselev (National Dragomanov University, Ukraine)
- David Krejcirik (Nuclear Physics Institute, Czech Academy of Sciences) "Non-self-adjoint graphs"
- Stefan Neukamm (TU Dresden, Germany) "Stochastic homogenization: An estimate for the two-scale expansion for correlated coefficients"
- Zhongwei Shen (University of Kentucky, USA) "Boundary regularity estimates in periodic homogenization"
- Jari Taskinen (University of Helsinki, Finland) "Spectral gaps for elastic and piezoelectric waveguides"
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Tatiana Suslina (St. Petersburg State University, Russia) "Spectral approach to homogenization of non stationary Schrödinger-type equations"
- Michael Vogelius (Rutgers University, USA)
- Ricardo Weder (IIMAS-UNAM, Mexico) Limiting absorption principle for singular solutions to Maxwell equations and plasma heating"
- Ian Wood (University of Kent, UK) "Spectral information contained in abstract M-functions''