Kirill Cherednichenko

NEW:

  • The paper by K. Cherednichenko, A. Kiselev, L. Silva (Operator Theory: Advances and Applications -- Volume dedicated to the memory of B. S. Pavlov) develops a quantitative framework for the analysis of boundary-value problems of mathematical physics, rooted in the works of M.S. Birman, M. G. Krein, M. I. Višik and inspired by a recent work of Vladimir Ryzhov (operator theorist and data scientist!) from the abstract operator-theoretic perspective. The final version of our manuscript is available on arXiv here.

  • A new master's programme MSc Mathematics with Data Science for Industry has been approved by Senate, to be launched in 2021/22. The MSc focuses on mathematical problem solving skills in an industrial context, with understanding and practical knowledge of data science. Please feel free to email me (at the address below) for further info. Watch this space for a link to the promotional campaign, which will be launched in October 2020. If you are into data science on its own as a statistics and computer science discipline, you may consider MSc Data Science and Statistics (Contact: Dr Jonathan Bartlett, jwb67 (at) bath.ac.uk) or MSc Data Science (Contact: Dr Marina De Vos, cssmdv (at) bath.ac.uk) if you are particularly interested in data science with emphasis on algorithms and programming.

  • Uzy Smilansky, Professor Emeritus at Weizmann Institute of Science, has been awarded a competitive David Parkin Visiting Professorship for 2020-21 and will visit Bath for 6 months in the coming academic year, travel restrictions due to COVID-19 permitting. Professor Smilansky is a recognised leader in several research areas on the physics-mathematics interface. He is known for raising important questions about the behaviour of complex system that have initiated substantial strands of research, as well as for solving open problems that have provided new insights.

  • Josip Žubrinić, who is moving towards the completion of his PhD project at the University of Zagreb, under the supervision of Igor Velčić, will visit the group for a period of three months in the spring of 2021, tentatively from 1 February to 30 April. 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 British Scholarship Trust.

  • The paper by K. Cherednichenko, A. Kiselev, Y. Ershova (Communications in Mathematical Physics) develops a new technique for the analysis of continuous media with resonant mictrostructures, providing explicit quantitaive information on the overall behaviour of composites ("dispersion relations"), which has been out of reach of the existing analytical methods. The paper links several research fields that have previously not been considered together, from time dispersive media on the physics side to the Birman-Krein-Vishik theory and generalised resolvents on the analysis side.

  • The paper by K. Cherednichenko, W. Graham (Philosophical Transactions of the Royal Society A) derives a generalisation of the Leontovich boundary condition on the boundary of a frequency-dispersive medium and analyses the associated surface waves.

  • The paper by K. Cherednichenko, Y. Ershova, and A. Kiselev (SIAM Journal on Applied Mathematics) provides a new machinery to obtain exact dispersion relations for resonant composites by asymptotic analysis.

  • Research seminar "Asymptotics, operators, and functionals'': Mondays at 16:15-18:45 on Zoom -- please let me know if you would like to join the email list for meeting links and videos of past talks.

    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.

    The next session will take place on 28 September -- the speaker is David Bourne

    Seminar programme

    Links to other seminars:

    One World PDE       London Analysis and Probability       Cardiff Analysis

    Here is a link to my EPSRC Fellowship "Mathematical foundations of metamaterials: homogenisation, dissipation and operator theory", which I held in 2014--2019.

    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)      Brief research statement (in PDF format)
    Research interests:

  • Rigorous analysis of problems in mechanics and electromagnetism
  • Homogenisation of partial differential equations and integral functionals
  • Applications of homogenisation to the mechanics of composite materials
  • Scale interaction effects in the description of the behaviour of heterogeneous media
  • Wave propagation in solid mechanics and electromagnetism
  • Dissipative operator theory and functional models
  • Scattering theory for differential equations with inhomogeneities
  • Asymptotic methods for periodic media with rapidly oscillating properties and for high-frequency problems
  • Variational methods in the mechanics of media with a microstructure
  • Theories for the description of dislocations as agents of plastic flow

    Research group

    Postdocs

    Reynaldo Castaneira, 2018--2019 (supported by UUKi Rutherford Fund)

    Yulia Ershova, 2016--2018

    James Roberts, Nov 2016 -- Mar 2017

    Marcus Waurick, 2015--2017 (now Chancellor's Fellow at the Unversity of Strathclyde)

    Shane Cooper, 2012--2013 (now Lecturer at University College London)

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

    Komil Kuliev, 2012--2013

    Current PhD students

    William Graham (2017--2021), working on waves in electromagnetic composites (member of the SAMBa CDT)

    Yi Sheng Lim (2019--2023), working on localisation phenomena for stochastic problems with resonant inclusions (member of the SAMBa CDT, supervised jointly with Hendrick Weber)

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

    Aaron Pim (2017--2021), working on homogenisation techniques for liquid crystals and existence theorems for associated energy functionals (Supervised jointly with Apala Majumdar and Jey Sivaloganathan)

    Former PhD students

    Matthew Lewis (Cardiff University, 2014--2018), Stability of solutions of a one-dimensional p-Laplace equation with periodic potential (Supervised jointly with Karl Michael Schmidt)

    James Evans (Cardiff University, 2012--2016): Higher-order homogenisation for Maxwell equations and on homogenisation and spectral properties of periodic thin structures with high contrast

    Collaborators

    Mikhail Cherdantsev (Cardiff University), Patrick Dondl (Universität Freiburg), Harsha Hutridurga (IIT Bombay) Alexander Kiselev (St.Petersburg), Karsten Matthies (Bath), Sergey Naboko (St.Petersburg), Frank Rösler (Cardiff), Luis Silva (IIMAS-UNAM, Mexico) Igor Velčić (Zagreb)

    Published articles            Submitted manuscripts             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

    MathSciNet       Research Gate       Google Scholar       Academic Profile on UoB site
    Past events:

  • BUC-XVIII 21--22 January 2020 (CIMAT, Unidad Mérida)

  • BUC-XVI: 2--6 September 2019 (IIMAS-UNAM, Mexico City)

  • Conference "Operators, Operator Families and Asymptotics II": 14--17 January 2019

  • BUC-XV: 16--19 September 2018 (CIMAT, Guanajuato, Mexico)

  • BUC-XII: 12--14 March 2018 (University of Bath)

  • BUC-XI: 27 November -- 3 December 2017 (CIMAT-Mérida)

  • BUC-VII: Spring School 30 March -- 3 April 2017 (UNAM), Workshop 4 April -- 7 April 2017 (CIMAT-Mérida)

  • Conference "Operators, Operator Families and Asymptotics": 16--19 May 2016

  • LMS-Bath-WIMCS Analysis Day: 4 December 2015