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

Welcome to the Data Science research using new topological methods for Materials Science, Computer Vision, Climate.

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

Topological data analysis : tools and applications
Affiliations : current positions and connections
News : success stories in the research group
Career highlights : achievements since 2005
Networks: AI Health, AAT meetings, MIF++
Grants : fellowships and research projects
Group in Topological Data Analysis: join us
Education : PhD (2003), MSc×2 and PGCert
Experience : CV and job history since 2000

Topological data analysis: tools and applications

theory and applications of topological data analysis

Videos of talks explaining key ideas, basic examples and various applications of Topological Data Analysis :

1-hour video of the talk "Skeletonization algorithms with theoretical guarantees for unorganized point clouds" at the online seminar of the Applied Algebraic Topology Research Network, 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.

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 £68 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).
Leader of the Intel Parallel Computing Center funded via the Big Data Center at the Lawrence Berkeley laboratory, US.
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.
Main organiser of the LMS-funded network Applied Algebraic Topology including Liverpool, Southampton, Queen Mary.
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:

News: success stories of the group in Topological Data Analysis

August 2019 : after the two workshops in March 2016 and August 2018, our group has hosted the 3rd annual workshop Mathematics for Materials Sciences in the MIF jointly with the group of Prof Herbert Edelsbrunner from IST Austria.
August 2019 : congratulations to Phil Smith for his first paper "Resolution-independent meshes of superpixels" accepted at ISVC 2019, to be published in LNCS proceedings.
August 2019 : received the Science Slam award (scanned) for the TED-style talk "The rise and fall of deep learning" to the public including more than 1000 participants of the European Crystallographic Meeting in Vienna (Austria).
August 2019 : gave the 30-min contributed talk "How to correctly sample unit cells in simulations of crystals" at the MathCryst (Mathematical and Theoretical Crystallography) meeting on 16-18 August 2019 in Vienna (Austria).
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)
- Lead of the group in Topological Data Analysis: 1 research assistant and 5+5+2 PhD students.
- Main organiser of the UK network Applied Algebraic Topology (since 2017) funded by the LMS.
- Training lead of the doctoral network in Artificial Intelligence for Future Digital Health (since 2019).
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 (2014), which is a top 3 conference in entire Computer Science and the highest h-index conference in any field.
- Best pure maths 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)
- Big Data Center (since 2017) led by Prabhat and funded by Intel at the Lawrence Berkeley National lab, US.
- Royal Society International Exchanges (2017-2019) with Prof Herbert Edelsbrunner's group at IST Austria.
- Industry secondments in the Computer Vision group (2014 - 2016) at Microsoft Research, Cambridge (UK).
Mentoring (all former members)
- Dr Alexey Chernov (postdoc in 2011-2012) is a Senior Lecturer in Statistics at Brighton University, UK.
- Dr Marjan Safi-Samghabadi (PhD student in 2009-2013) is a lecturer at International Imam Khomeini University, Iran.

Grants (larger than 10K GBP in value), see also smaller grants

	EPSRC grant awarded under the call New Approaches to Data Science jointly with Principal Investigators Prof Ulrike Tillmann and Dr Heather Harrington from Oxford and a team from Swansea. The 100% budget is more than £3.5M over 2018 - 2022. I've led the Computer Science team at Liverpool with a budget over 715K GBP including Prof Andrew Cooper, Paul Spirakis, Igor Potapov. The success has led to the creation of the Centre for Topological Data Analysis and was highlighted in the university news. Title : Application-driven Topological Data Analysis (ref. EP/R018472/1).
	Unilever's top-up (18K GBP since March 2019) 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.
	The Royal Society International Exchanges (IES/R2/170039, 12K GBP until December 2019) for bilateral visits between the TDA group at Liverpool (UK) and Prof Herbert Edelsbrunner's group at IST Austria.
	Intel gift (80K USD) for Grzegorz Muszynski's PhD "Topological analysis of the Climate System" funded through the Lawrence National Berkeley lab (US) from April 2017 at the University of Liverpool, UK.
	Knowledge Transfer Secondments at Microsoft Research Cambridge with Dr Andrew Fitzgibbon. 2014 - 2016 : EPSRC gave about 24K GBP, Microsoft Research provided 75K GBP in-kind contribution. Title : Applications of Topological Data Analysis to Computer Vision. Covered visits to Prof Carlsson at Stanford University (US) and Ayasdi, to Prabhat at Lawrence National Laboratory in Berkeley (2016).
	EPSRC first grant (100K GBP) with post-doctoral assistant Dr Alexey Chernov, 2011 - 2013 Title : Persistent Topological Structures in Noisy Images (ref. EP/I030328/1), which continued as Knowledge Transfer Secondments at Microsoft Research Cambridge in 2014-2016.
	Marie Curie International Incoming Postdoctoral Fellowship (142K Euros) Combinatorial Knot Theory. University of Liverpool (UK), September 2005 - May 2007.
	Postdoctoral Fellowship (22K Euros) on Combinatorial Group Theory at University of Burgundy, Dijon (France), December 2003 - November 2004.

Group in Topological Data Analysis : 1 research assistant and 5+5+2 PhD students

The group leads a development of new geometric and topological methods that will enable next generation materials discovery. The key difference with past discrete tools (such as symmetry groups) is a continuous (stable-under-noise) approach to a mathematical classification of crystals. The following success stories have appeared in the news.

In April 2019 the research of our group in the MIF has been highlighted in the case study The shape of spaces.
In 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.
In January 2018 the EPSRC awarded £3.5M to the 5-year project Application-Driven Topological Data Analysis in 2018 - 2022 (EP/R018472/1) at the Universities of Liverpool, Oxford, Swansea. The Liverpool team has a budget over £715K.
In 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.
The photo below was taken in February 2018. Members from left to right: Naohiko Ban, Asim Munshi, Eris Tricker, Krasen Samardzhiev, Vitaliy Kurlin, Grzegorz Muszynski, Philip Smith.
The recent photo from the 3rd Mathematics for Materials workshop includes new members and visitors from IST Austria.

Research Assistant Cristian Badoi is a software developer in the Materials Innovation Factory, funded by the Leverhulme Research Centre for Functional Materials Design over July 2019 - April 2020.

Cristian is originally from Romania, has completed a good 3rd year research project in 2018-19 and a short project under my supervision funded by a Faculty bursary in summer 2019 at Liverpool.

5 graduate students who I help as the first supervisor (ordered by their start date)

	PhD student Mr Grzegorz Muszynski (since April 2017) is supervised by Dr Vitaliy Kurlin (80%) and the Senior Staff Scientist Michael Wehner, funded by the Intel Parallel Computing Center. Grzegorz has a split-site supervision agreement and spends July-December at the NERSC in the Berkeley lab (US). Project : Topological Analysis of the Climate System. Grzegorz has gained a Computer Science degree from the Technical University of Warsaw in 2016.
	PhD student Mr Philip Smith (since October 2017) is supervised by Dr Vitaliy Kurlin (80%) and Prof Igor Potapov, funded by the Leverhulme Centre at the Materials Innovation Factory in Liverpool. Project : New Computational Methods for a Faster Materials Discovery. Phil has gained a first class 4-year degree in mathematics from Durham University in 2017 and also learned C++ programming skills during his summer projects under my supervision in 2016-17.
	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 Shan Luo, funded by the school of EEE&CS as the support for the EPSRC grant EP/R018472/1. Project : New Topological and Geometric Methods for Computer Vision problems in Materials Science. 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.

5 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, Dr Vitaliy Kurlin (40%), Prof Graeme Day, funded by the Leverhulme Centre at the Materials Innovation Factory. 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 Materials Innovation Factory. Project : Data Driven Discovery of Functional Molecular Co-crystals. Katerina has two degrees: BSc in Electrical Engineering (Greece), BSc+MSc in Chemistry (York, UK).

2 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.
	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

Short-term project students in 2018-19: Cristian Badoi (3rd year), Samuel Ball (4th year), Ruilin Han (3rd year), Yuhao Hua (3rd year), Di Liu (3rd year), Kristian Rowan (3rd year), Yijia Zhao (3rd year).

The group offers the opportunity to give informal talks at the regular group seminar.

You could also explore the former students and postdocs of the research group.

Join the group in Topological Data Analysis

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.

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

Mexican PhD Scholarships (the webpage in Spanish).
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).
AXA postdoctoral fellowships (deadlines in early April/October).
Leverhulme Trust Early Career Fellowships (deadlines in February-March).
EPSRC Postdoctoral Fellowships (no deadline, best submitted in January or July).
Royal Society Newton International Fellowships (deadlines in February-March, extra fellowships for candidates from Israel, China, Italy, Brazil, Mexico, South Africa, Turkey).

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.

Experience : CV and job history since 2000

Vitaliy Kurlin's curriculum vitae (pdf, 5 pages, 270K, last updated in June 2019)
Current research : Topological Data Analysis for Materials Science, Computer Vision, Climate
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.

Dr Vitaliy Kurlin: mathematics & computer science

Current research: topological data analysis. Everything is possible!

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