Dr Vitaliy Kurlin: mathematics & computer science

Welcome to the Data Science research developing new geometric and topological methods for Materials Science.

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 theory and applications

Videos of talks explaining key ideas, basic examples and various applications of Geometric and Topological Data Science

• Introduction to Periodic Geometry and Topology (44 min) at Geometry and Topology behind fabrics (online), May 2021.
• Introduction to Periodic Geometry (25 min) at MACSMIN: Maths & Computer Science for Materials Innovation, Sep 2020.
• The mergegram of a dendrogram (24 min) at Mathematical Foundations of Computer Science (online), August 2020.
• Peristence-based image skeletonization (30 min) at the SIAM symposium Topological Image Analysis (online), June 2020.
• Skeletonization algorithms with theoretical guarantees for unorganized point clouds (1 hour) at AATRN (US), May 2018.
• Topological methods for a faster materials discovery (47 min) at Applied Topology, Bedlewo (Poland), June 2017.
• 1-min video spotlight at CVPR 2014 (Computer Vision and Pattern Recognition), Columbus, Ohio (USA), June 2014.
• Applications of Topological Data Analysis to Computer Vision (1h), Microsoft Research, Cambridge (UK), February 2014.
• Reconstruction of plane graphs from noisy samples (1 hour), Informatics Forum, Edinburgh University, April 2013.

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Affiliations: current positions and connections

• Data Scientist at the Materials Innovation Factory (University of Liverpool) funded by Unilever, HEFCE, Leverhulme, ERC. MIF is a new £82 million institute spun out from the 1st Chemistry department in the UK for 4*/3* research (2nd overall).
• Senior Lecturer (Associate Professor) in the 1st Computer Science department in the UK for 4*/3* research (10th overall).
• Consultant of the International Union of Crystallography commission on Mathematical and Theoretical Crystallography.
• Co-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 Topological Data Analysis centre between Universities of Oxford, Liverpool, Swansea.
• See other past and current admin posts. Many thanks to the following research sponsors and collaborators:
                 

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

• June 2021 : gave the talk "Introduction to Periodic Geometry and Topology" at the Geometric Topology Workshop 2021.
• June 2021 : group walk in Sefton park. The names below are from left to right (a nearly reversed order is accidental :-).
  
  First : Teddy, Katerina, Matt, Phil, Hannah, Olga, Vitaliy. Second : Olga, Vitaliy, Hannah, Phil, Matt, Katerina, Teddy.
• June 2021 : selected as a consultant of the IUCr commission on Mathematical and Theoretical Crystallography.
• June 2021 : congratulations to my former PhD student Dr Philip Smith, who has passed his viva with minor corrections. Here is the praise from the PhD examiners: "We believe that the degree is well-deserved and wish all the best to Phil with his next challenges!" Phil started the postdoctoral position funded by the NERC grant led by Dr Thomas McDonald.
• May 2021 : co-organised the mini-symposium Computational Geometry, Topology and Symmetry meet Materials Science at SIAM MS 2021 featuring our group members Olga Anosova, Phil Smith, Marco Mosca, Matt Bright, Dan Widdowson.
• May 2021 : presented the paper An isometry classification of periodic point sets published in proceedings of DGMM.
• May 2021 : gave the invited talk "Introduction to Periodic Geometry and Topology" (44-min video) at the workshop Geometry and Topology behind fabrics at multiple scales (online).
• Since March 2013 : previous news stories are in the news archive.

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

• Major leadership roles (all admin roles)
  • Lead of the group in Data Science theory and applications (since 2017) : two PhD graduates, one postdoc and 6+6+3 PhD students. In 2020 we established the new area of Periodic Geometry and Topology for materials applications.
  • Co-director and training lead of the doctoral network in Artificial Intelligence for Future Digital Health (since 2019).
  • Founder of the annual conference MACSMIN = Maths and Computer Science for Materials Innovation (since 2020).
• Prestigious awards (all grants)
  • Marie Curie International Incoming Postdoctoral Fellowship (2005 - 2007), University of Liverpool, UK.
  • Teaching award : one of 3 final nominees in the Science Faculty for a Lecturer of the Year award (2013).
• Main research papers (all publications)
  • Best applied paper introducing the Homologically Persistent Skeleton in Computer Graphics Forum (2015).
  • Best conference (peer-reviewed) paper on hole detection in 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.
  • Best pure maths 59-page paper : V. Kurlin, Compressed Drinfeld associators, Journal of Algebra (2005).
• Keynote talks (all presentations)
  • Best public talk : The rise and fall of deep learning received the Science Slam award (scanned) at ECM 2019.
  • Keynote applied maths talk : Topological Computer Vision at Prospects in Data Science (January 2016).
  • Highest profile pure maths talk : 20-min oral at International Congress of Mathematicians 2006, Madrid.
• Major collaborations (all co-authors)
  • The Royal Society International Exchanges grant (2017-2019) with Prof Herbert Edelsbrunner's group at IST Austria led to the joint SoCG 2021 paper and helped to establish the new research area of Periodic Geometry and Topology.
  • The work with Climate Scientists via the Big Data Center (2017-2021) funded by Intel at the Lawrence Berkeley lab (US) led to the highly cited articles GMD, JGRA on the Atmospheric River Tracking Method Intercomparison Project (ARTMIP).
  • Industry secondments in the Computer Vision group (2014 - 2016) at Microsoft Research in Cambridge (UK) led to the new method superpixel over-segmentations of images in joint papers in ISVC and Journal of Electronic Imaging.
• Mentoring (all former members)
  • Dr Marjan Safi-Samghabadi (PhD student in 2009-2013) is a computer programmer in Tehran, Iran.
  • Dr Alexey Chernov (postdoc in 2011-2012) is a Senior Lecturer in Statistics at Brighton University, UK.
  • Dr Grzegorz Muszynsky (PhD student in 2017-2021) is a Data Scientist in the AI lab, BAS, Cambridge, UK.
  • Dr Philip Smith (PhD student in 2017-2021) is a postdoctoral researcher on the NERC grant in Liverpool, UK.

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

	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 Dr 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. The 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.

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Group in Data Science theory and applications : 1 postdoc and 6+6+3 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.
 

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.

• 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 budget over £715K.
• August 2017 : the group has established the Intel Parallel Computing Centre (IPCC) funded at the University of Liverpool by Intel as a part of 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.

	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 in Russia. With Viktor we are going to co-supervise a new PhD student 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 in Russia and the UK.
	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. Publications: PR 2021, SoCG 2021, ISVC 2019.

Current 1st supervision : six 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 (80%) 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 Dr Matthew Bright (since October 2019) is supervised by Dr Vitaliy Kurlin (80%) and MIF director Prof Andy Cooper (20%), funded as the support for the EPSRC grant. Project : Geometry and topology for a continuous similarity between crystals. Matthew has obtained a PhD in molecular biology at Manchester, gained data analysis experience at Royal Mail and USS, also completed a maths MSc thesis under my supervision in summer 2018.
	PhD student Mr Daniel Widdowson (since October 2020) is supervised by Dr Vitaliy Kurlin (60%), Prof Andy Cooper (20%) and Dr Angeles Pulido (20%), funded by the network AI in 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 (40%), MIF director Prof Andy Cooper (30%), Dr Angeles Pulido (20%), Dr Jason Cole (10%), funded by the CCDC and 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.

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Current 2nd supervision : six 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 Fraser Holloway (since October 2017) is supervised by Dr Laura Harkness-Brennan and Dr Vitaliy Kurlin (40%), funded by the Big Data Science Centre for Doctoral Training in Physics. Project : Topological Data Analysis methods for AGATA (a gamma-ray detector). Fraser has completed a BSc degree in Physics 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 Ms Katerina Vriza (since October 2018) is supervised by Dr Matthew Dyer, Dr Vitaliy Kurlin (20%), funded by the CCDC and Leverhulme Research Centre at the MIF. Project : Data Driven Discovery of Functional Molecular Co-crystals. Katerina has two degrees: BSc in Electrical Engineering (Greece), BSc+MSc in Chemistry (York, UK).
	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 in 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.

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Current 3rd supervision : four 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.

Short term students in 2020-21 : Jiahui An (3rd year), Gan Fang (3rd year), Xuhui Gong (3rd year), Zhaoyu Han (3rd year), Yuelin Jiang (3rd year), Yang Li (3rd year), Jakob Ropers (3rd year), Haoran Xu (3rd year), Yang Yang (3rd year).

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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).

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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 (Russia), 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 (Russia), 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 (Russia), 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 (Russia), 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.

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Experience : CV and job history since 2000

• Vitaliy Kurlin's curriculum vitae (pdf, 6 pages, 254K, last updated in September 2019)
• Current research : Geometric and Topological Data Science with applications to Materials Science
• 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 (associate professor), Computer Science and 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, Russia
• 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, Russia
• October 2000 - June 2001 : C++ programmer in traffic recognition, TochMash Module, Moscow, Russia.

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