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Geometry and topology for a continuous similarity between crystals

  • Full or part time
  • Application Deadline
    Sunday, March 24, 2019
  • Funded PhD Project (European/UK Students Only)
    Funded PhD Project (European/UK Students Only)

Project Description

The vision of the project is to transform materials discovery into a routine computational task. Materials discovery still needs a lot of human expertise, trial-and-error and even pure luck, because there is no rigorous theory to guide an efficient search in the huge space of all theoretically possible materials. Any solid crystalline material (briefly, a crystal) will be modelled as a periodic structure formed by embedded graphs based on repeated patterns of atoms or ions.

The project will develop a new continuous approach to a much more efficient discovery of crystals by answering the following fundamental question. Given two periodic structures, how similar are they to each other, more exactly what is a quantifiable distance between them? Progress in any field should be justified by reliable measurements. Hence any new crystal should be tested for similarity with already known structures. To enable this comparison and to reveal a continuous hierarchy of existing crystals, a well-defined distance between crystals is needed.


The student will be based in the Department of Computer Science or the new £68M research institute MIF (Materials Innovation Factory) within the University of Liverpool, UK. The supervisor is Dr Vitaliy Kurlin (, whose group includes one postdoctoral assistant and five PhD students working on crystals. The step-by-step advice is provided at The project can be considered as a part of the new Centre for Topological Data Analysis (, joint with the Universities of Oxford and Swansea) funded by the recent £3.5M EPSRC grant "Application-driven Topological Data Analysis" (EP/R018472/1,

The Centre for Topological Data Analysis will study the shape of data, through the development of new mathematics and algorithms, and build on existing data science techniques in order to obtain and interpret the shape of data. Modern science and technology generates data at an unprecedented rate. A major challenge is that this data is often complex, high dimensional, may include temporal and/or spatial information. A theoretical field of mathematics that enables the study of shapes is geometry and topology. The ability to quantify the shape of complicated objects is only possible with advanced mathematics and algorithms.

Prior Experience

Applications are welcomed from students with a 2:1 (60% grade point average) or higher masters or BSc degree or equivalent in Mathematics, Statistics, Computer Science or Computational Chemistry. The essential requirements are programming experiences (Python or C/C++) and excellent communication skills to work in a large team. The project will involve a close collaboration with colleagues from different areas and industry partners, e.g. AI3SD (Artificial Intelligence for Science Discovery network at the University of Southampton), CCDC (Cambridge Crystallographic Data Centre) and IBM Research at the Hartree Centre in the Daresbury lab close to Liverpool.

How to apply

Enquiries can be sent to before making a formal application. Applications can be submitted as described at Applications should list Dr Vitaliy Kurlin as the potential supervisor and choose the option "School funded PhD" when asked how you will fund the PhD. Applications must contain a cover letter, a curriculum vitae or resume, copies of undergraduate and graduate transcripts, a 1-2 page research statement describing how the applicant’s qualifications and research interests would fit the project, a copy of the applicant’s bachelor or master’s thesis and the names and contact information of academic references.

Funding Notes

The PhD is funded for 3 years from October 2018 by the school of Electrical Engineering, Electronic and Computer Science at the University of Liverpool (UK). The funding of 20K GBP per year covers the tuition fees for UK/EU students (about 4.2K GBP per year) and a tax-free bursary. Additional travel funds can be available from various grants in the university for presenting research work at top conferences.

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