We aim to discuss the latest results and techniques in the asymptotic analysis of operators, differential equations and functionals, as well as its applications to mechanics, materials and wave propagation. The talk will usually focus on one or two aspects of a problem of current interest, and is meant to form the basis for an informal discussion during and after the talk. All welcome.

Next talk is by Yulia Ershova on 4 July 2016.

Dates and venue: 23--28 May 2016, Department of Mathematical Sciences, University of Bath. Room: 4W 1.1

Information on timetable to follow.

Course title: ``High-velocity estimates, inverse scattering and topological effects''. Link to course outline. Professor Weder's visit is supported by University of Bath and EPSRC.

** 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)

**Confirmed speakers: **

- 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"
- Jari Taskinen (University of Helsinki, Finland) "Spectral gaps for elastic and piezoelectric waveguides"
- Tatiana Suslina (St. Petersburg State University, Russia) "Spectral approach to homogenization of non stationary Schrödinger-type equations"
- Ricardo Weder (IIMAS-UNAM, Mexico) "Limiting absorption principle for singular solutions to Maxwell equations and plasma heating"
- 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''

**Programme committee: **

Kirill Cherednichenko (Bath), Fritz Gesztesy (Missouri), Peter Kuchment (Texas A&M), Marco Marletta (Cardiff), Graeme Milton (Utah), Leonid Parnovsky (UCL)

**Conference summary:**

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.

I am EPSRC Fellow and Reader in Mathematics

Here is a link to my 5-year EPSRC-supported project "Mathematical foundations of metamaterials: homogenisation, dissipation and operator theory"

I am always happy to talk to anyone looking for a PhD project. Here are some of the possible research topics.
Please feel free to email me at * K.Cherednichenko (at) bath.ac.uk* if you are interested.

My curriculum vitae (in PDF format) List of my publications (in PDF format)

Shane Cooper, 2012--2013 (now EPSRC Research Fellow at the University of Bath)

Mikhail Cherdantsev, 2008--2010 (now Lecturer at Cardiff University)

James Evans (Cardiff University, 2012-2015), working on higher-order homogenisation for Maxwell equations and on homogenisation and spectral properties of periodic thin structures with high contrast

Matthew Lewis (Cardiff University, 2014-2017), working on eigenvalue problems for the nonlinear p-Laplace equation and its versions with rapidly oscillating coefficients (Supervised jointly with Karl Michael Schmidt)

Serena D'Onofrio (University of Bath, 2016-2020), working on new analytical techniques in homogenisation and scattering for composite media

Michel Bellieud (Université Montpellier 2), Richard Craster (Imperial), Alexander Kiselev (Kyiv), Karsten Matthies (Bath) Graeme Milton (Utah), Stefan Neukamm (TU Dresden), Luis Silva (UNAM), Valery Smyshlyaev (UCL), John Willis (Cambridge), Vasily Zhikov (Vladimir)

* Journal articles: *

* Submitted papers: *

* Papers in preparation: *

**Employer:** Department of Mathematical Sciences,
University of Bath
**Job Title:** Reader in Mathematics
**Telephone:** +44 1225 38 6891

**E-mail Address:** K.Cherednichenko (at) bath.ac.uk

**Postal Address:**

Department of Mathematical Sciences

University of Bath

Claverton Down

Bath, BA2 7AY

United Kingdom

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