I organised the conference ``Operators, Operator Families and Asymptotics'' at the University of Bath,
from Monday 16 May to Thursday 19 May 2016.
List of registered participants
Conference poster: larger version
The conference is supported by London Mathematical Society, University of Bath, EPSRC, and Bath Institute for Mathematical Innovation (BIMI)
- Yves Capdeboscq (University of Oxford, UK)
"Small volume asymptotics for Maxwell's equations"
- Giuseppe Cardone (University of Sannio, Italy)
"Boundary perturbations of planar waveguides: oscillating boundary, windows, non-periodic perforations''
- Maxence Cassier (University of Utah, USA)
"On the spectral theory and limiting amplitude principle for a transmission problem between a dielectric and a metamaterial''
- Tanya Christiansen (University of Missouri, USA) "Sharp lower bounds on a resonance counting function in even-dimensional Euclidean scattering"
- Shane Cooper (University of Bath, UK) "Asymptotic analysis of stratified elastic media in the space of functions with bounded deformation"
- 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"
- 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"
- Andrii Khrabustovskyi (Karlsruhe Institute of Technology, Germany)"On the spectrum of a class of periodic quantum graphs"
- Alexander Kiselev (National Pedagogical Dragomanov University, Ukraine) "On the connections between the spectral theory of quantum graphs and homogenisation problems in low-dimensional structures"
- 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"\li>
- Jari Taskinen (University of Helsinki, Finland) "Spectral gaps for elastic and piezoelectric waveguides"\li>
- Tatiana Suslina (St. Petersburg State University, Russia)
"Spectral approach to homogenization of non stationary Schrödinger-type
- Ricardo Weder (IIMAS-UNAM, Mexico) "Limiting absorption principle for singular solutions to Maxwell equations and plasma
- Aaron Welters (Florida Institute of Technology, USA) "Analyticity of the Dirichlet-to-Neumann map for Maxwell's equations in passive composite media"
- Ian Wood (University of Kent, UK) "Spectral information contained in abstract M-functions''
Kirill Cherednichenko (Bath), Fritz Gesztesy (Missouri), Peter Kuchment (Texas A&M), Marco Marletta (Cardiff), Graeme Milton (Utah), Leonid Parnovsky (UCL)
The conference is aimed at making 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.