Prof Vitaliy Kurlin: mathematics & computer science

Data Science theory and applications. Everything is possible!

E-mail: vitaliy.kurlin(at)gmail.com, University of Liverpool, UK

Brief profile: a universal scientist, a mathematician by training, professor in computer science, and the lead of the group developing a new area of Geometric Data Science for crystallography, materials chemistry, and structural biology.

Contents


Geometric Data Science : from theory to applications and back

Data Science Theory and Applications

Geometric Data Science develops continuous parametrisations for moduli spaces of real data objects under practically important relations. The key example is a cloud of unordered points under rigid motion. Until CVPR 2023, these clouds did not have complete invariants with continuous metrics and polynomial-time algorithms even for 4 points in the plane.

The major breakthroughs are the Crystal Isometry Principle and a polynomial-time extension of the SSS theorem to unordered points in any dimension, underpinned by the publications in JACS, NeurIPS, CVPR, ICML from the top 25 list.


Videos of talks explaining the latest results in Geometric Data Science, see also earlier videos

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Affiliations : current positions and connections

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News : success stories of the group in Data Science Theory and Applications

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Highlights : research, leadership, awards, papers, keynotes, collaborations, mentoring

Research : developing the new area of Geometric Data Science


Major leadership roles (all administrative roles)

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Personal awards (all research grants)

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10 main research papers where I was a single author or a lead author (all publications)

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Keynote talks (all conference presentations)

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Major collaborations (all co-authors)

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Mentoring (all former members)

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Grants (larger than £10K), see also smaller grants

EPSRC logo 2024 - 2032 Co-I in the Centre for Doctoral Training in Digital and Automated Materials Chemistry.
EPSRC logo 2024 - 2029 Co-I in the hub AI for Chemistry: Alchemy, joint with Imperial College London.
Royal Society logo 2024 - 2026 The Royal Society International Exchanges grant (£12K) for bilateral visits between our Data Science group and Prof Yoshua Bengio (Mila institute, Montreal, Canada), the Alan Turing award winner (Computer Science analog of Nobel's laureate) with the highest h-index in Computer Science.

Title : Generative methods for materials design on geographic-style maps of crystals (IES\R1\241474).
Royal Society logo 2023 - 2025 The Royal Society APEX fellowship replacing the teaching for two years (£100K).
Title : New geometric methods for mapping the space of periodic crystals (ref APX\R1\231152).
Outline. In 1869, Mendeleev arranged the known chemical elements into a spatial map – the periodic table - which grouped them according to their properties. The appearance of ‘gaps’ in the table spurred the discovery of new elements, while the attempt to understand the physical rationale behind its structure drove revolutionary advances in both physics and chemistry. We aim to extend Mendeleev’s idea to all periodic structures using spatial relationships between atomic nuclei.
Royal Society logo 2023 - 2025 The Royal Society International Exchanges grant (£12K) for bilateral visits between our Data Science group at Liverpool and Prof Nicholas Kotov's lab at the University of Michigan (US).

Title : Geometric invariants for interactions of proteins with inorganic nanoparticles (IES\R3\223215).
EPSRC logo 2022 - 2025 New Horizons EPSRC grant with co-I Prof Andy Cooper FRS.
Budget : £250K covers a postdoctoral assistant for 20 months.
Title : Inverse design of periodic crystals (ref EP/X018474/1).
RAEng logo 2021 - 2023 Royal Academy of Engineering Fellowship, Cambridge Crystallographic Data Centre.

Title : Data Science for Next Generation Engineering of Solid Crystalline Materials (ref IF2122\186).

The RAEng funded a 2-year teaching replacement (total £220K), the CCDC invested £60K for a PDRA.
NERC logo 2020 - 2023 NERC grant (£965K, ref NE/V010778/1) on improving plastic packaging is led by Dr Thomas McDonald. I am responsible for a Data Science analysis of plastic materials properties.
Title : Post-Consumer Resin - Understanding the quality-performance linkage for packaging.
Unilever logo 2019 - 2022 Unilever's top-up (£18K) for the PhD bursary of Thomas Welsh, who has done a great MSc thesis for Unilever in summer 2018 and continues working on Unilever's projects in his PhD.
EPSRC logo 2018 - 2023 EPSRC grant led by Prof Ulrike Tillmann and Prof Heather Harrington from Oxford. The 100% budget is £3.5M. I lead the Liverpool team with a budget over £715K including Professors Cooper, Spirakis, Potapov. This success has created the Centre for Topological Data Analysis.
Title : Application-driven Topological Data Analysis (ref EP/R018472/1).
Intel logo 2017 - 2020 Intel gift ($40K per year) for Grzegorz Muszynski's PhD "Topological analysis of the Climate System" funded via the Lawrence National Berkeley lab (US) at the University of Liverpool.
Royal Society logo 2017 - 2019 The Royal Society International Exchanges grant (£12K) for bilateral visits between our Data Science group at Liverpool and Prof Herbert Edelsbrunner's group at IST Austria.

Title : Topological Data Analysis for a faster discovery of new materials (IES/R2/170039).
Microsoft logo 2014 - 2016 Knowledge Transfer Secondments at Microsoft Research Cambridge with Dr Andrew Fitzgibbon. The EPSRC gave about £25K, Microsoft Research provided £75K in-kind contribution.

Covered visits to Prof Carlsson at Stanford and Lawrence National Laboratory in Berkeley (2016).

Title : Applications of Topological Data Analysis to Computer Vision.
EPSRC logo 2011 - 2013 EPSRC first grant (£125K) with post-doctoral assistant Dr Alexey Chernov, which continued as Knowledge Transfer Secondments at Microsoft Research Cambridge in 2014-2016.
Title : Persistent Topological Structures in Noisy Images (ref EP/I030328/1)
EC logo 2005 - 2007 Marie Curie International Incoming Postdoctoral Fellowship (142K Euros).

University of Liverpool (UK), September 2005 - May 2007.

Title : Combinatorial Knot Theory.
Dijon logo 2003 - 2004 Postdoctoral Fellowship (22K Euros).

University of Burgundy, Dijon (France).

Title : Combinatorial Group Theory.

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Group in Data Science Theory and Applications (DSTA) : members and PhD students

March 2023 : Dan Widdowson, Viktor Zamaraev, Matt Bright, Vitaliy, Olga Anosova, Will Jeffcott, Jonathan Balasingham

DSTA group photo March 2023

The group develops a new area of Geometric Data Science studying moduli spaces of real data objects modulo practical equivalences. The key example is a finite or periodic set of unordered points modulo rigid motion or isometry. The major breakthroughs are the Crystal Isometry Principle for all periodic crystals and complete isometry invariants of all clouds of m unordered points with continuous metrics that are computable in polynomial time in m for a fixed Euclidean dimension.

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Group members, postdoctoral assistants and associate members

Viktor Zamaraev's photo Associate member Dr Viktor Zamaraev is a Senior Lecturer in the Department of Computer Science.

Viktor had postdoctoral positions at Durham and Warwick after earning a PhD in Theoretical Computer Science. With Viktor we supervise PhD student Jonathan Balasingham since October 2021.

Joint papers : Scientific Reports 2024, Integrating Materials and Manufacturing Innovation 2024.
Olga Anosova's photo University Teacher Dr Olga Anosova in the department of Computer Science, University of Liverpool. Olga completed a PhD in Dynamical Systems and taught big classes at several universities since 2005.

Papers: MATCH 2025, IUCrJ 2024, JMIV 2023, DGMM 2022, CMMP 2022, DAMDID 2022, DGMM 2021, NumGrid 2021.
Daniel Widdowson's photo Postdoctoral assistant Dr Daniel Widdowson is funded by the AIchemy hub.

In 2020 - 2024, Daniel completed the PhD "Continuous Isometry Invariants of Periodic Crystal Structures" supervised by Vitaliy Kurlin (70%) and Andy Cooper (20%), and Isaac Sugden (10%).

Papers : CGD 2024, DiD 2023, CVPR 2023, NeurIPS 2022, JACS 2022, DiD 2022, MATCH 2022.
Yury Elkin's photo Research assistant Dr Yury Elkin was funded by the EPSRC grant Inverse design of periodic crystals.

In 2017 - 2022, Yury completed the PhD A new compressed cover tree for k-nearest neighbour search and the stable-under-noise mergegram supervised by Vitaliy Kurlin and Marja Kankaanrinta.
Joint papers : ICML 2023, TopoInVis 2022, Mathematics 2021, MFCS 2020, TopoInVis 2019.

Miloslav Torda's photo Associate member Dr Miloslav Torda is a postdoc in Andy Cooper's group.

In 2018-2022, Milo completed the PhD Maximally dense crystallographic symmetry group packings for molecular crystal structure prediction supervised by Yannis Goulermas, Vitaliy Kurlin, Graeme Day.

Joint papers : SISC 2023, PRE 2022

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Current 1st supervision : students who I help as the first supervisor (ordered by start date).

Jonathan McManus' photo PhD student Mr Jonathan (Teddy) McManus (since October 2020) is supervised by Vitaliy Kurlin (60%), MIF director Andy Cooper (30%), and Isaac Sugden (10%), funded by the CCDC and the Leverhulme Research Centre at the Materials Innovation Factory.

Project : Towards prediction of synthetically accessible organic molecular crystals.
Jonathan has obtained a BSc in Mathematics from Durham University, gained industry experience in Data Science and completed a short project in Liverpool under my supervision in summer 2020.
Jeffcott Will's photo PhD student Mr William Jeffcott (since November 2021) is funded by the CDT in Distributed Algorithms and supervised by Vitaliy Kurlin.

Paper: MATCH 2025.

Project : Data Science and Artificial Intelligence for smart sustainable plastic packaging.
Will completed a 1st class Master of Mathematics degree at Durham, UK.

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2nd supervision : students who I help as the 2nd supervisor (ordered by start date).

Jonathan Balasingham's photo PhD student Mr Jonathan Balasingham (since October 2021) is supervised by Viktor Zamaraev, Vitaliy Kurlin, MIF director Andy Cooper, and Isaac Sugden (Cambridge Crystallographic Data Centre, UK).

Project : AI-based exploration of crystal spaces to accelerate drug discovery.
Jonathan completed MSc in Scientific and Data-Intensive Computing (University College London), MSc in Industrial Engineering (San Jose State University) and BSc in Computer Science (University of California, Santa Cruz). Papers: Scientific Reports 2024, IMMI 2024.

Adam Coxson's photo PhD student Mr Adam Coxson (since October 2021) is supervised by Alessandro Troisi and Vitaliy Kurlin.

Project : Developing Machine Learning algorithms with physical constraints for materials discovery.

Adam completed a first class Master of Physics degree at the University of Manchester, UK.

Alessandro Gerada's photo PhD student Mr Alessandro Gerada (since October 2021) is supervised by William Hope, Vitaliy Kurlin and Steve Patterson, funded by the doctoral network AI for Future Digital Health.

Project : Understanding bacterial resistance by machine learning from genetic data.
Alessandro has a medical degree from the University of Malta and several qualifications from the Royal Colleges of Pathologists and Physicians (UK).

Nandini Gadhia's photo PhD student Ms Nandini Gadhia (since December 2021) is supervised by Anh Nguyen, Vitaliy Kurlin and Dominic Richards, funded by the doctoral network AI for Future Digital Health.

Project : Artificial Intelligence for accelerated drug discovery.
Nandini has MSc in Physics (UCL) and BSc in Maths and Physics (Warwick). She does a part-time PhD in parallel with her work at the STFC Hartree centre.

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3rd supervision : students who I help as the 3rd supervisor (ordered by start date).

Sam Carruthers' photo PhD student Mr Sam Carruthers (since October 2019) is supervised by the MIF director Andy Cooper (80%) and Vitaliy Kurlin (10%).

Project : Mobile robot chemists for autonomous solar fuels research.

Sam completed a 4-year degree in Chemistry at Liverpool, UK.

Michael Walker's photo PhD student Mr Michael Walker (since October 2019) is supervised by the MIF director Andy Cooper, Vitaliy Kurlin, Yue Wu and Ellen Piercy (Unilever).

Project : Vision-based estimation of viscosity, bubble distributions and impurities of liquids.

Michael completed a BSc degree in Physics.

Danny Ritchie's photo PhD student Mr Danny Ritchie (since October 2021) is funded by Chemistry and supervised by Matthew Dyer, Vladimir Gusev, Vitaliy Kurlin, and Matt Rosseinsky.

Project : Machine learning, mathematical optimisation and algorithmic techniques for materials.

Danny completed a 1st class degree in Physics at the University of Manchester, UK.

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Join the group in Data Science Theory and Applications

If you know C++ or Python, and wish to apply for a PhD studentship or a postdoctoral fellowship at Liverpool, e-mail me.

Funded PhD studentship in the MIF from October 2025, eligible for international students

    .
  • PhD project. Explaining structure-property relations in the materials space [based on Geometric Data Science].
  • Supervisors. Prof Vitaliy Kurlin, Prof Andy Cooper FRS (academic director of the Materials Innovation Factory).
  • Start date October 2025. Duration 4 years. UKRI bursary £18,622 per year (not taxed, will likely increase). Why Liverpool?
  • Deadline: mid-January 2025. Before applying, please e-mail your informal enquiries to Vitaliy Kurlin as soon as possible.
  • Requirements. Strong background in mathematics or computer science. Programming skills. Chemistry is not essential.
  • About 15 students in Digital and Automated Materials Chemistry will get a cohort-based training, including Data Science.
  • Description. The definition of isostructural crystals remained incomplete until a crystal structure was defined as a rigid class of all crystal representations that can be matched by rigid motion [1]. The resulting continuous space of all periodic structures was parametrised by generically complete invariants [2] that distinguish all non-duplicate periodic materials in the Cambridge Structural Database (CSD) and can be inverted to any generic 3D structure [3]. These invariants predicted a new material by structural analogy [4] and achieved state-of-the-art results in materials property prediction [5].
    While past approaches often used black-box predictions, this project requires mathematical and computational skills to explain functional properties such as structural energy, gas adsorption or potential for photocatalysis in terms of the developed ultra-fast invariants [1-5]. Any property can be visualised as a mountainous landscape on geographic-style maps obtained by projecting the materials space to analytic invariant coordinates. Local optima on such landscapes will indicate the regions where target properties can be improved by modifying crystal structures in an optimal way.
    [1] O.Anosova, V.Kurlin, M.Senechal. The importance of definitions in crystallography, IUCrJ 2024.
    [2] D.Widdowson, V.Kurlin. Continuous invariant-based maps of the CSD, Crystal Growth & Design 2024.
    [3] D.Widdowson, V.Kurlin. Resolving the data ambiguity for periodic crystals, NeurIPS 2022.
    [4] Q.Zhu et al. Analogy powered by prediction and structural invariants, JACS 2022.
    [5] J.Balasingham et al. Accelerating material property prediction using isometry invariants, Scientific Reports 2024.

External funding: we look for postdoctoral candidates with mathematical and programming skills.

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Education : PhD (2003), MSc (2000, 2002), and PGCert (2009)

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Experience : CV and job history since 2000

  • Vitaliy Kurlin's curriculum vitae (pdf, 10 pages, last updated in December 2024)
  • Current research : Geometric Data Science for computer vision, materials chemistry, and structural biology
  • Past research : climate science, non-commutaive algebra, low-dimensional topology, graph embeddings
  • Programming : C/C++ (industry level), Python, PHP, HTML5, CSS3, Python, Java, Matlab, Javascript
  • Since 2016 : senior lecturer, then reader, now full professor, Materials Innovation Factory, Liverpool, UK
  • 2014 - 2016 : visiting scientist in the Computer Vision group at Microsoft Research, Cambridge, UK
  • 2007 - 2013 : university lecturer (assistant professor) in Mathematics, Durham University, UK
  • June - September 2007 : research postdoc in Sensor Networks, Lancaster University, UK
  • September 2005 - May 2007 : research postdoc in Knot Theory, University of Liverpool, UK
  • February - May 2005 : teaching postdoc in Knot Theory, Independent University of Moscow, Russia
  • December 2003 - November 2004 : postdoc in Combinatorial Group Theory, University of Burgundy, France
  • November 2000 - October 2003 : PhD student in Geometry and Topology at Moscow State University, Russia

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