Kirill Cherednichenko

Kirill's research interests are in a variety of areas within the wide subject area of multiscale analysis, where the predominant approach is the asymptotics of solutions of differential equations. During the 23 years of his research career (since the time he was an undergraduate student at St.Petersburg State University, Russia), he has made progress in understanding the emergence of higher-order effects in the overall behaviour of composites, discovered and described a number of phenomena in wave propagation, introduced a number of new techniques in the mathematical analysis of nonlinear composites, and most recently, obtained a series of results on operator-norm convergence of solutions to problems of periodic homogenisation.

Josip Žubrinić

Josip, who is moving towards the completion of his PhD project at the University of Zagreb, under the supervision of Igor Velčić, is visiting the group until July 2021. Josip's research focusses on the analysis of thin elastic structures and operator norm-resolvent estimates in homogenisation. Josip's visit to Bath will be supported by the British Scholarship Trust and the London Mathematical Society.

Serena D'Onofrio

Serena, who is in the final year of her PhD studies at Bath, works on the analysis of differential operators on periodic singular and thin structures, which can be represented, for example, by appropriate periodic measures. Serena has proved operator-norm resolvent convergence for scalar version of such operators in the long-wave regime ("homogenisation") and has subsequently extended [arXiv, arXiv] her technique to the case of Maxwell's equations of electromagnetism.

Aaron Pim

Aaron's research is focused on new approaches to the description of defects in liquid crystals, using asymptotic analysis of PDE in domains with singular boundaries. Aaron is in the final year of his PhD project, during which he has studied the behaviour of solutions to the Laplace equation in a punctured square domain with piecewise-constant boundary conditions and developed a new variational approach to the analysis of defects in liquid crystals. He is currently applying his techniques to understanding the effective properties of periodic arrays of defects.

Will Graham

Will joined the group as a summer project student in 2016, and since September 2017 have has been working on a research project as part of the SAMBa Centre for Doctoral Training. Will's interests are in wave propagation through periodic structures, at the triple point of photonic crystal fibres, spectral analysis, and numerical analysis. Hi is co-supervised by Kirill Cherednichenko, Chris Bowen and David Bird

Prior to his current project, Will carried out an analysis of the interface conditions between a dielectric and a Lorentz medium in the context of Maxwell's equations of electromagnetism (a version of the so-called Leontovich conditions) and has studied the waves propagating along the interface and decaying exponentially away from it. He has also studied numerically the related dispersion relations.

Yi Sheng Lim

Yi Sheng is interested in a range of questions on the probability-analysis interface. His PhD project is focussed on spectral properties of PDEs with random coefficients, in particular in the context of Anderson localisation and spectral phase transitions from extended to localised states. In his work he uses a variety of techniques from stochastic analysis, asymptotic analysis, homogenisation, and operator theory.

Yulia Ershova

Yulia is a specialist in the spectral analysis of quantum graphs, which occupy an intermediate position between one-dimensional (ODE) and multi-dimensional (PDE) differential operators. During her PhD studies at the Institute of Mathematics of NAS (Kyiv), Yulia solved the problem of the reconstruction of the topology of a finite graph from its spectrum and, in particular, described what graphs are isospectral.

Reynaldo Castaneira

Reynaldo is a UUKi Rutherford Fellows from the Technical University of Oaxaca, Mexico. His research has been focussed on the use of variational techniques for the study of solutions to the n-body problem. In his research project at Bath, Reynaldo develops a new approach to nonlinear problems in homogenisation using recent ideas in the analysis of operators describing time-dispersive media.

Forthcoming highlights: