Dr Vitaliy Kurlin: research and teaching in mathematics and computer science

The war in Ukraine should finish as soon as possible otherwise many more people can die across the world.

Our group is developing the new area of Periodic Geometry for applications in crystallography and materials.

If you are a potential postdoc, PhD student or intern with C++ or Python skills, read how to join the group.

Data Science research : theory and applications
Affiliations : current positions and connections
News : success stories in the research group
Career highlights : achievements since 2005
Grants : fellowships and research projects
Research group in Data Science : join us
Networks: AI Health, AAT meetings, MIF++
MACSMIN=Maths+CS for Materials Innovation
Education : PhD (2003), MSc×2 and PGCert
Experience : CV and job history since 2000

Data Science research : from theory to applications and back

Videos of talks explaining key ideas and applications of Data Science, see also earlier videos

The Crystal Isometry Principle (44 min) at the LIV.DAT seminar in the Physics department at Liverpool, April 2022.
The Crystal Isometry Principle (48 min) at MACSMIN: Maths & Computer Science for Materials Innovation, Sep 2021.
A unique and continuous code of all periodic crystals (16 min) at MS-65 of the IUCr congress (online), August 2021.
Introduction to invariant-based machine learning for periodic crystals (20 min) at the IUCr congress, August 2021.
Introduction to Periodic Geometry and Topology (32 min) at the Geometric Topology Workshop (online), June 2021.

Affiliations: current positions and connections

Data Scientist at the Materials Innovation Factory (University of Liverpool) funded by Unilever, HEFCE, Leverhulme, ERC. MIF is a £82 million institute spun out from a top 3 Chemistry department in the UK for outstanding (4*) research impact.
Reader (Associate Professor) in the top 5 Computer Science department in the UK for outstanding (4*) research outputs.
Industrial Fellow at the Cambridge Crystallographic Data Centre, funded by the Royal Academy of Engineering, UK.
Consultant of the International Union of Crystallography commission on Mathematical and Theoretical Crystallography.
Director of the Doctoral Network in Artificial Intelligence (AI) for Future Digital Health funded by the University of Liverpool to train the next generation of world-leading experts in AI to solve data intensive problems in healthcare.
Management team member of the Centre for Topological Data Analysis at Universities of Oxford, Liverpool, Swansea.
See other past and current admin posts. Many thanks to the following research sponsors and collaborators:

News: success stories of the group in Data Science theory and applications

May 2022 : invited to give a talk at the 32nd International Symposium on Chirality on 17-20 July in Chicago, US.
May 2022 : the IUCr 2023 approved the micro-symposium on crystal comparisons co-chaired with Marjorie Senechal
May 2022 : congratulations to Dan as a key contributor to the paper "Analogy Powered by Prediction and Structural Invariants: Computationally-Led Discovery of a Mesoporous Hydrogen-Bonded Organic Cage Crystal" accepted by JACS.
April 2022 : presented the Crystal Isometry Principle at the LIV.DAT seminar in the Physics department at Liverpool, UK.
April 2022 : congratulations to PhD student Will Jeffcott on completing the 179km cycling Tour of Flanders in Belgium!
April 2022 : presented the Crystal Isometry Principle at the British Crystallographic Association conference: summary.
April 2022 : warm congratulations to Dr Katerina Vriza on the PhD viva and starting her postdoctoral position in Leeds!
Since March 2013 : previous news stories are in the news archive.

Career highlights : leadership, awards, papers, keynotes, collaborations, mentoring

Major leadership roles (all admin roles)
- Since 2020 : founder of the annual conference MACSMIN = Mathematics and Computer Science for Materials Innovation.
- Since 2019 : training lead, now the director of the UoL doctoral network in Artificial Intelligence for Future Digital Health.
- Since 2017 : leading the group in Data Science theory and applications, including two postdocs and many PhD students.
Personal awards (all grants)
- 2021 - 2023 : Royal Academy of Engineering Industry Fellowship at the Cambridge Crystallographic Data Centre, UK.
  Title : Data Science for Next Generation Engineering of Solid Crystalline Materials (ref IF2122\186).
- 2013 : Teaching award Lecturer of the Year, voted by Durham Student's Union in the Science Faculty.
- 2011 - 2013 : PI of the EPSRC project EP/I030328/1, the first grant on Topological Data Analysis in the UK.
- 2005 - 2007 : Marie Curie International Incoming Postdoctoral Fellowship, University of Liverpool, UK.
Main research papers (all publications)
- 2022 : Fundamental invariants for mapping all periodic crystals in MATCH Comm. Math. Computer Chemistry.
- 2020 : A visual map for the space of inorganic compositions featured on the cover page in Chemistry of Materials.
- 2015 : Homologically Persistent Skeleton in Computer Graphics Forum, extended in AAM, Pattern Recognition (2021).
- 2014 : first successful Computer Science paper in peer-reviewed Proceedings of Computer Vision and Pattern Recognition CVPR 2014, which is a top 3 conference in entire Computer Science and the highest h-index conference in any field.
- 2005 : my longest 59-page single-authored paper in pure maths Compressed Drinfeld associators, Journal of Algebra.
Keynote talks (all presentations)
- 2019 : public talk The rise and fall of deep learning won the Science Slam award at European Crystallographic Meeting.
- 2016 : keynote applied maths talk on Topological Computer Vision at Prospects in Data Science, Southampton, UK.
- 2006 : high-profile pure maths talk (20-min oral) at the International Congress of Mathematicians, Madrid, Spain.
Major collaborations (all co-authors)
- Since 2021 : developing an impact case funded by the RAEng Fellowship at the CCDC. Over two CPU-days our invariants detected five physically impossible pairs among 660K+ periodic crystals in the CSD, now investigated by five journals.
- Since 2017 : collaboration with the world-leading materials scientists Andy Cooper and Matt Rosseinsky at the MIF. The joint papers in MATCH, DACOMSIN, Chemical Science, Chemistry of Materials amplified the impact of Periodic Geometry.
- 2017 - 2021 : the Royal Society International Exchanges grant with Prof Herbert Edelsbrunner's group at IST Austria led to the joint SoCG 2021 paper and helped us to establish the new research area of Periodic Geometry and Topology.
- 2017 - 2021 : collaboration with climate scientists via the Big Data Center funded by Intel at the Lawrence Berkeley lab (US) led to the highly cited articles in GMD and JGRA on the Atmospheric River Tracking Method Intercomparison Project.
- 2014-2016 : industry secondments in the Computer Vision group at Microsoft Research in Cambridge (UK) led to the new method superpixel image over-segmentations described in joint papers in ISVC and Journal of Electronic Imaging.
Mentoring (all former members)
- PhD student in 2017-2021 : Dr Philip Smith is a postdoc on the NERC grant at the Unversity of Liverpool, UK.
- PhD student in 2017-2021 : Dr Grzegorz Muszynsky is a postdoc in Machine Learning at Oxford, UK.
- postdoc in 2011-2012 : Dr Alexey Chernov is a Senior Lecturer in Statistics at Brighton University, UK.
- PhD student in 2009-2013 : Dr Marjan Safi-Samghabadi is a computer programmer in Tehran, Iran.

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

	Royal Academy of Engineering Industrial Fellowship at the 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 grant (£965K, 2021-2023, 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's top-up (£18K, 2019-2021) 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 grant led by Prof Ulrike Tillmann and Prof Heather Harrington from Oxford. The 100% budget is £3.5M over 2018 - 2023. 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).
	The Royal Society International Exchanges grant (£12K over 2017-2019) 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).
	Intel gift ($40K per year) for Grzegorz Muszynski's PhD "Topological analysis of the Climate System" (2017-2020) funded through the Lawrence National Berkeley lab (US) at the University of Liverpool.
	Knowledge Transfer Secondments at Microsoft Research Cambridge with Dr Andrew Fitzgibbon. 2014 - 2016 : 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 first grant (£125K) with post-doctoral assistant Dr Alexey Chernov (2011 - 2013), which continued as Knowledge Transfer Secondments at Microsoft Research Cambridge in 2014-2016. Title : Persistent Topological Structures in Noisy Images (ref. EP/I030328/1)
	Marie Curie International Incoming Postdoctoral Fellowship (142K Euros). University of Liverpool (UK), September 2005 - May 2007. Title : Combinatorial Knot Theory.
	Postdoctoral Fellowship (22K Euros). December 2003 - November 2004. University of Burgundy, Dijon (France). Title : Combinatorial Group Theory.

Group in Data Science theory and applications : two postdocs and many more PhD students

The photo below was taken in October 2019 : Cameron Hargreaves, Matt Bright, Vitaliy Kurlin, Georg Osang (visitor from IST Austria), Philip Smith, Cristian Badoi, Yury Elkin, Katerina Vriza, Miloslav Torda, Marco Mosca, Thomas Welsch.

TDA group photo February 2018

The group develops the new area of Periodic Geometry and Topology to enable next generation materials discovery. The key difference with past discrete tools (such as symmetry groups) and trial-and-error random searches is a continuous (stable-under-noise) approach to the isometry classification of crystals. The following successes appeared in the news.

October 2021 : the Royal Academy of Engineering Industrial Fellowship "Data Science for Next Generation Engineering of Solid Crystalline Materials" at the Cambridge Crystallographic Data Centre was announced in the university news.
April 2019 : the research of our group in the MIF has been highlighted in the case study The shape of spaces.
December 2018 : the research of PhD student Grzegorz Muszynski funded by Intel through the Big Data Center at the Lawrence Berkeley lab (US) has been highlighted in the HPC wire news Topology Can Help Us Find Patterns in Weather.
January 2018 : the EPSRC awarded £2.8M to the 5-year project Application-Driven Topological Data Analysis in 2018 - 2023 (EP/R018472/1) at the Universities of Liverpool, Oxford, Swansea. The Liverpool team has a £700K+ budget.
August 2017 : the group has established the Intel Parallel Computing Centre (IPCC) funded by Intel at the University of Liverpool via the Big Data Center at the Berkeley lab to develop new methods for detecting extreme weather events.
Since 2017 : the group offers the opportunity to give informal talks at the regular group seminar, see our alumni.

	Associate member Dr Viktor Zamaraev is a Lecturer in Computer Science since October 2019. 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.
	Associate member Dr Olga Anosova is a research assistant in Applied Data Science since October 2020 in the department of Public Health, Policy and Systems at Liverpool. Olga completed a PhD in Dynamical Systems and worked as a teacher and lecturer at several universities. Joint papers: CMMP 2022, DACOMSIN 2021, DGMM 2021, NumGrid 2020.
	Research assistant Dr Philip Smith is funded by the NERC grant to improve plastic packaging. In 2013-2017 Phil completed a 4-year Master of Mathematics degree at Durham, where we worked together on a summer project in Computer Vision funded by the London Mathematical Society. In 2017-2021 Phil completed the PhD "Geometric and Topological Methods for Applications to Materials and Data Skeletonisation" under my supervision. Joint papers: PR 2021, SoCG 2021, ISVC 2019.
	University Teacher Dr Matthew Bright is replacing my teaching and project supervision in 2021-2022. In October 2019 Matt started his PhD supervised by Dr Vitaliy Kurlin (80%) and MIF director Prof Andy Cooper (20%), which was extended until 2023 due to his teaching replacement job in 2021-2022. Project : Geometry and topology for a continuous similarity between crystals. Matt obtained a PhD in molecular biology in 2000, gained industry experience and completed MSc thesis under my supervision in summer 2018. Joint papers: CMMP 2022, NumGrid 2020, CaG 2020.

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

	PhD student Mr Yury Elkin (since November 2017) is supervised by Dr Vitaliy Kurlin (80%) and Dr Marja Kankaanrinta, funded by the school of EEE&CS at Liverpool. Yury has a split-site supervision agreement and spends 6 months every year (summer/winter vacations) at the University of Helsinki. Project : Topological methods in shape recognition. Yury has gained strong mathematical skills in his 4-year degree at the University of Helsinki, Finland.
	PhD student Mr Marco Mosca (since October 2018) is supervised by Dr Vitaliy Kurlin (80%) and the MIF director Prof Andy Cooper, funded by the EEE&CS to develop an impact case with the CCDC. Project : Discovering hidden patterns in high-dimensional data for materials science. Marco has gained a degree in Computer Science and Bioinformatics at the University of Bologna, Italy.
	PhD student Mr Thomas Welsch (since January 2019) is supervised by Dr Vitaliy Kurlin (60%) and Dr Patrick Totzke, funded by the school of EEE&CS as the support for the EPSRC grant EP/R018472/1. Project : Programme synthesis and genetic programming. Thomas has gained Computer Science degrees: BSc from Tennessee (US), then completed an excellent MSc thesis under my supervision in Liverpool on an image processing project important for Unilever.
	PhD student Mr Daniel Widdowson (since October 2020) is supervised by Dr Vitaliy Kurlin (70%) and Prof Andy Cooper (20%), and Dr Jason Cole (10%) funded by the network AI for Future Digital Health. Project : A rigorous identification of all metastable polymorphs for better and safer drugs. Daniel has obtained a BSc in Mathematics from Warwick University and also completed his MSc thesis in Liverpool under my supervision in summer 2020.
	PhD student Mr Jonathan (Teddy) McManus (since October 2020) is supervised by Dr Vitaliy Kurlin (60%), MIF director Prof Andy Cooper (30%), and Dr Jason Cole (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.
	PhD student Mr Danny Ritchie (since October 2021) is funded by Chemistry and supervised by Dr Vitaliy Kurlin, Prof Matt Rosseinsky, Dr Matthew Dyer, Dr Mike Gaultois and Dr Vladimir Gusev. Project : Machine learning, mathematical optimisation and algorithmic techniques for materials. Danny has completed a 1st class degree in Physics at the University of Manchester, UK.
	PhD student Mr William Jeffcott (since November 2021) is funded by the CDT in Distributed Algorithms and supervised by Dr Vitaliy Kurlin, Dr Thomas McDonald and Dr Louise Connell. Project : Data Science and Artificial Intelligence for smart sustainable plastic packaging. Will has completed a 1st class Master of Mathematics degree at Durham, UK.

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

	PhD student Mr Krasen Samardzhiev (since October 2017) is supervised by Dr Daniel Arribas-Bel, Dr Vitaliy Kurlin (40%) and Prof Alex Singleton, funded by the Data Analytics and Society CDT. Project : A Topological Data Analysis of Big Spatio-Temporal Urban Data. Krasen has completed a BSc degree in Computer Science at Liverpool, UK
	PhD student Mr Miloslav Torda (since October 2018) is supervised by Prof Yannis Goulermas (40%), Dr Vitaliy Kurlin (40%), Prof Graeme Day (20%), funded by the Leverhulme Centre in the MIF. Project : Analysis of energy landscapes of molecular crystal structures employing combinatorial and topological methodologies. Milo has gained two 5-year degrees in Psychology and Mathematics/Probability at Bratislava (Slovakia).
	PhD student Mr Cameron Hargreaves (since October 2018) is supervised by Dr Matthew Dyer and Dr Vitaliy Kurlin (40%), funded by the SOLBAT project (a part the Industrial Strategy Challenge Fund). Project : Data Science and Machine Learning for the Discovery of Solid Lithium Ion Conductors. Cameron has completed BSc in Electrical Engineering and MSc in Computer Science at Liverpool.
	PhD student Mr Muizdeen Raji (since November 2019) is supervised by Prof Nagesh Kalakonda (50%), Dr Vitaliy Kurlin (30%), Prof Joseph Slupsky (20%), funded by the AI for Future Digital Health. Project : Cellular diversity in health and disease using mass cytometry and computational approaches. Muizdeen is originally from Nigeria, has a BSc in Chemistry and an MSc in Biomedical Sciences.
	PhD student Mr Jonathan Balasingham (since October 2021) is supervised by Dr Viktor Zamaraev, Dr Vitaliy Kurlin and Prof Andy Cooper. Project : AI-based exploration of crystal spaces to accelerate drug discovery. Jonathan has 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).
	PhD student Mr Adam Coxson (since October 2021) is supervised by Prof Alessandro Troisi and Dr Vitaliy Kurlin. Project : Developing Machine Learning algorithms with physical constraints for materials discovery. Adam has completed a first class Master of Physics degree at the University of Manchester, UK.
	PhD student Mr Alessandro Gerada (since October 2021) is supervised by Prof William Hope, Dr Vitaliy Kurlin and Prof 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).
	PhD student Ms Nandini Gadhia (since December 2021) is supervised by Dr Anh Nguyen, Dr Vitaliy Kurlin and Dr 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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Current 3rd supervision : graduate students who I help as the 3rd supervisor (ordered by their start date).

	PhD student Mr Shiyamjith Nathaniel (since October 2018) is supervised by Prof Robert Page (50%), Dr Laura Harkness-Brennan (25%) and Dr Vitaliy Kurlin (25%), funded by the Big Data Science CDT. Project : Machine learning and data analysis for gamma-ray detectors. Shiyam has completed a BSc degree in Physics at Liverpool, UK.
	PhD student Mr Sam Carruthers (since October 2019) is supervised by the MIF director Prof Andy Cooper (80%), Dr David Marquez-Gamez (10%) and Dr Vitaliy Kurlin (10%). Project : Mobile robot chemists for autonomous solar fuels research. Sam has completed a 4-year degree in Chemistry at Liverpool, UK.
	PhD student Mr Michael Walker (since October 2019) is supervised by the MIF director Prof Andy Cooper, Dr David Marquez-Gamez, Dr Vitaliy Kurlin, Dr Yue Wu and Ellen Piercy (Unilever). Project : Vision-based estimation of viscosity, bubble distributions and impurities of liquids. Michael has completed a BSc degree in Physics.

Join the group in Data Science theory and applications

If you know C++ or Python, and wish to join as an intern, PhD or postdoc, please read the post how to join the group.

We are especially looking for postdoctoral candidates with excellent communication skills and external funding.

If you follow the advice, we'll support your application for a PhD studentship or a postdoctoral fellowship below.

Royal Society Newton International Fellowships (deadlines in February-March, extra fellowships for postdoctoral candidates from Israel, China, Italy, Brazil, Mexico, South Africa, Turkey).
European Marie Curie individual fellowships (deadlines usually in early September).
EPSRC Postdoctoral Fellowships (no deadline, best submitted in January or July).
Leverhulme Trust Early Career Fellowships (deadlines in February-March).
AXA postdoctoral fellowships (deadlines in early April/October).
PhD scholarships at the University of Liverpool (different deadlines depending on your country and case).
Commonwealth PhD Scholarships (for low and middle income countries, deadlines in February/March).

Education : PhD (2003), MSc×2 and PGCert

PGCert : Postgraduate Certificate in Teaching and Learning in Higher Education (2008 - 2009) and full membership of the Higher Education Academy, UK.
PhD in Geometry and Topology, Moscow State University, November 2000 - October 2003
Thesis : Basic embeddings of graphs and 3-page embeddings of graphs.
Supervisors : Prof Victor Buchstaber and Prof Arkady Skopenkov.
MSc in Mathematics, Independent University of Moscow, 1995 - 2002 (part-time)
Thesis : Turaev-Viro invariants of compact 3-dimensional manifolds.
MSc in Mathematics (grade point average 5.0/5), Moscow State University, September 1995 - June 2000
Thesis : 3-page diagrams of spatial 3-valent graphs.
Gold medal (top grades 5/5 in all subjects), Physical-Mathematical School N146, Perm, June 1995.
Top grades in mathematics and physics in the 2-year distance course by Moscow Institute of Physics and Technology (September 1993 - May 1995) whose famous graduates include the Nobel laureates A. Geim and K. Novoselov.

Experience : CV and job history since 2000

Vitaliy Kurlin's curriculum vitae (pdf, 4 pages, 97K, last updated in February 2022)
Current research : Periodic Geometry and Topology, Data Science for materials applications
Past research : geometric topology, graph theory, singularity theory, non-commutative algebra
Programming skills : C/C++ (industry level), PHP, HTML5, CSS3, Python, Java, Matlab, Javascript
Since 2016 : senior lecturer, then reader (associate professor), Materials Innovation Factory, Liverpool
2014 - 2016 : visiting scientist in the Computer Vision group at Microsoft Research, Cambridge (UK)
2007 - 2013 : university lecturer (assistant professor) in Pure Mathematics, United Kingdom
June - September 2007 : research postdoc in Sensor Networks, University of Lancaster, 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
December 2003 - November 2004 : research postdoc in Combinatorial Group Theory, University of Burgundy, France.
November 2000 - October 2003 : PhD student in Geometry and Topology at Moscow State University

Dr Vitaliy Kurlin: mathematics & computer science

Data Science theory and applications. Everything is possible!

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