Selected 10 papers in top journals and conferences
 2024 : V. Kurlin.
Mathematics of 2dimensional lattices.
Foundations of Computational Mathematics, a top 15 publication venue in Computational Mathematics.
This paper finally resolved discontinuities of 2dimensional lattice bases (up to rigid motion) and continuously parametrised moduli spaces of lattices up to isometry and rigid motion (composed with uniform scaling) in dimension 2.
 2023 : Y. Elkin, V. Kurlin.
A new nearlinear time algorithm for knearest neighbor search using a compressed cover tree.
Proceedings of ICML: International Conference on Machine Learning, a top 20 publication venue across all subjects.
This paper justified a nearlinear parametrised complexity for nearest neighbour search in any metric spaces.
 2023 : D. Widdowson, V. Kurlin.
Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants.
Proceedings of CVPR: Computer Vision and Pattern Recognition, a top 4 publication venue across all subjects.
This paper extended the isometry classification of triangles to arbitrary clouds of unlabeled points in any Euclidean space.
 2023 : M. Bright, A. Cooper, V. Kurlin.
Geographicstyle maps for 2dimensional lattices.
Acta Crystallographica Section A, a top 12 publication venue in Crystallography.
This paper presented the first continuous maps of (millions of) 2dimensional lattices from real crystals in the Cambridge Structural Database.
 2022 : D. Widdowson, V. Kurlin.
Resolving the data ambiguity for periodic crystals.
Proceedings of NeurIPS 2022: Neural Information Processing Systems, a top 10 publication venue across all subjects.
This paper justified the Crystal Isometry Principle extending Mendeleev's table to a continuous space of periodic crystals.
 2022 : Q. Zhu, J. Johal, D. Widdowson, Z. Pang, B. Li, C. Kane, V. Kurlin, G. Day, M. Little, A. Cooper.
Analogy Powered by Prediction and Structural Invariants.
J Amer. Chem. Soc. 2022, 144, 22, 9893–9901.
This paper in a top 25 publication venue across all subjects reported new material predicted by invariants from NeurIPS.
 2021 : P. Smith, V. Kurlin.
Skeletonisation algorithms for unorganised point clouds with high levels of noise.
Pattern Recognition, v.115 (2021), 107902.
This paper proves guarantees for a Homologically Persistent Skeleton (HoPeS), a key contribution to Topological Data Analysis in a top 10 publication venue in Computer Vision.
 2014 : V. Kurlin.
A fast and robust algorithm to count topologically persistent holes in noisy clouds.
Proceedings of CVPR 2014:
Computer Vision and Pattern Recognition, p. 14581463.
This paper is in a top 4 publication venue across all subjects, the highest hindex conference in any field.
 2008 : C. Kearton, V. Kurlin.
All 2dimensional links live inside a universal 3dimensional polyhedron.
AGT : Algebraic and Geometric Topology, v. 8 (2008), no. 3, p. 12231247.
This highly cited paper in a top 15 publication venue in Geometry developed the singularity theory for 2dimensional links.
 2005 : V. Kurlin.
Compressed Drinfeld associators.
Journal of Algebra, v. 292 (2005), no. 1, p. 184242.
This paper in a top 10 venue in Algebra proved a short formula for log(e^x e^y) modulo commutators of commutators.
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2024
2023
2022
2021
2020
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20162018
20112015
20082010
20052007
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Geometric Data Science develops geographicstyle maps and polynomialtime algorithms for moduli spaces of data objects considered modulo practically important equivalence relations.
The first solved case (based on papers in
FoCM 2024,
ACA 2023,
Chirality 2023)
is the space of 2dimensional lattices modulo rigid motion and uniform scaling, parametrised as a unit square whose vertices (0,0) and (0,1) represent all square and hexagonal lattices, resp. After identifying the boundary sides, this space becomes a 2D sphere whose equator represents all mirrorsymmetric 2D lattices.
Other major objects are unordered point clouds, e.g. clouds of atomic centres in a molecule, geometric graphs, e.g. molecular graphs in 3D and abstract graphs in metric spaces, and periodic point sets modelling solid crystalline materials, all considered under isometry (any distancepreserving transformation).
In the image: the benzene is represented by the hexagonal cloud of carbon atoms without hydrogens; the water molecule is represented by the graph with one oxygen and two hydrogens;
the table salt NaCl is represented by a cubic lattice of sodium and chlorine ions.

 The image shows the kite in the middle (in green and yellow) and the trapezium at the bottom (in red, yellow, and blue) whose sets of 4 vertices are indistinguishable by 6 pairwise distances. This pair motivated the stronger new invariants.
 Geometric Data Science is presented in the tutorials at
SIAM MDS (2 hours),
FANeSy (1.5 hours), IMSI (1 hour) and minisymposia at
the European Congress of Mathematics (2 hours) and Mathematical Aspects of Materials Science (4 hours).
 The latest work on continuous isometry invariants and computable metrics for finite and periodic point sets is regularly discussed at the annual conference MACSMIN, the weekly MIF++ seminar on zoom, and the DSTA group seminar.
The draft book Introduction to Periodic Geometry and Topology (June 2021 version) will be updated in autumn 2024.
 Finite sets :
2page summary of complete isometry invariants of Euclidean ndimensional clouds of unordered points.
2page summary of persistence vs easier, faster, and stronger isometry invariants of point clouds in any metric space.
Simplexwise Distance Distributions for finite spaces with metrics, the latest pdf, an early version in arxiv:2303.14161
The strength of a simplex for a classification of Euclidean clouds: the latest pdf, an early version in arxiv:2303.13486
 1periodic case :
Continuous metrics on 1periodic sequences, pdf (July 2024), an early version in arxiv:2205.04388
 3periodic case :
2page summary of the Crystal Isometry Principle justifying a materials genome for periodic crystals
A complete isometry classification of 3dimensional lattices, the latest pdf, an early version in arxiv:2201.10543
Welcome to a continuous world of 3dimensional lattices, the latest pdf, an early version in
arxiv:2109.11538
 Any dimension :
Pointwise Distance Distributions of periodic sets, the latest pdf, an early version in arxiv:2108.04798
Recognition of nearduplicate periodic patterns by continuous metrics, the latest pdf, an early version in arxiv:2205.15298

Since 2020 : new area Geometric Data Science
for applications in computer vision, chemistry, and structural biology
 Since 2011 Applied Mathematics for Topological Data Analysis, Computer Vision, and Climate Science
 19992010 Pure Mathematics : topology, graphs, noncommutative algebra
 2008  2010 :
singularity theory related to knots and links
 2005  2007 :
postdoctoral work on noncommutative algebra
 2001  2004 :
PhD work on classifications of embedded graphs
 1999  2000 : MSc work
on link invariants and basic embeddings
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 Jonathan Balasingham, Viktor Zamaraev, Vitaliy Kurlin.
 Accelerating Material Property Prediction using Generically Complete Isometry Invariants.
 Scientific Reports, v.14 (10132), 2024.

[11 pages, 1.5M]
[project page]
[reference]


 Vitaliy Kurlin.
 Polynomialtime algorithms for continuous metrics on atomic clouds of unordered
points.
 MATCH Communications in Mathematical and in Computer Chemistry, v.91 (2024), p.79108.
 [30 pages, 1M]
[project page]
[reference]


 Philip Smith, Andy McLauchlin, Tom Franklin, Peiyao Yan, Emily Cunliffe, Tom Hasell, Vitaliy A Kurlin, Colin Kerr, Jonathan Attwood, Michael P Shaver, Tom O McDonald.
 A datadriven analysis of HDPE postconsumer recyclate for sustainable bottle packaging.
 Resources, Conservation and Recycling, v.205 (2024), 107538.

[11 pages]
[project page]
[reference]

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 Yury Elkin, Vitaliy Kurlin.
 A new nearlinear time algorithm for knearest neighbor search using a compressed cover tree.
 ICML 2023 (International Conference on Machine Learning), p. 92679311.
Top 20 publication venue across all subjects including Nature and Science.
 [45 pages, 615K]
[project page]
[reference]


 Dan Widdowson, Vitaliy Kurlin.
Video (8 min)
Poster (pdf)
 Recognizing rigid patterns of unlabeled point clouds by complete and continuous isometry invariants with no false negatives and no false positives.
 Proceedings of CVPR 2023 (Computer Vision and Pattern Recognition), 12751284.
Top 4 publication venue across all subjects including Nature and Science.
Extended version of section 3 for metric spaces:
[latest pdf]
Extended version of section 4 for Euclidean spaces:
[latest pdf]

[10 pages, 1.4M]
[project page]
[reference]


 Matt Bright, Andy Cooper, Vitaliy Kurlin.
 Continuous chiral distances for 2dimensional lattices.
 Journal Chirality, v.35 (12), p.920936 (2023).
 Special issue of the International Symposium on Chirality 2022.

[17 pages, 4.2M]
[project page]
[reference]


 Daniel SchwalbeKoda, Dan Widdowson, Tuan Anh Pham, Vitaliy Kurlin.
 Inorganic synthesisstructure maps in zeolites with machine learning and crystallographic distances.
 Digital Discovery, v.2(6), p.19111924 (2023), doi:10.1039/D3DD00134B.
 [30 pages, 1M]
[project page]
[reference]


 Milo Torda, John Goulermas, Roland Púček, Vitaliy Kurlin.
 Entropic trust region for densest crystallographic symmetry group packings.
 SIAM Journal on Scientific Computing, 2023, v.45(4), p.B493B522.

[accepted version, 52 pages, 21M]
[project page]
[reference]


 C.Hargreaves, M.Gaultois, L.Daniels, E.Watts, V.Kurlin, M.Moran, Y.Dang, R.Morris, A.Morscher, K.Thompson, M.Wright, B.Prasad, F.Blanc, C.Collins, C.Crawford, B.Duff, J.Evans, J.Gamon, G.Han, B.Leube, H.Niu, A.Perez, A.Robinson, O.Rogan, P.Sharp, E.Shoko, M.Sonni, W.Thomas, A.Vasylenko, L.Wang, M.Rosseinsky, M.Dyer.
 A Database of Experimentally Measured Lithium Solid Electrolyte Conductivities Evaluated with Machine Learning. npj Computational Materials, v.9, 9 (2023).

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 Milo Torda, John Goulermas, Vitaliy Kurlin, Graeme Day.
 Densest plane group packings of regular polygons.
 Physical Review E, v. 106 (5), 054603.

[13 pages, 372K]
[project page]
[reference]


 Qiang Zhu, Jay Johal, Dan Widdowson, Zhongfu Pang, Boyu Li, Christopher M Kane, Vitaliy A Kurlin, Graeme M Day, Marc Little, Andrew I Cooper.
 Analogy Powered by Prediction and Structural Invariants: ComputationallyLed Discovery of a Mesoporous HydrogenBonded Organic Cage Crystal.
 JACS (J Amer. Chem. Society), 2022, 144, 22, 9893–9901.

[9 pages, 3M]
[project page]
[reference]


 Dan Widdowson, Marco M Mosca, Angeles Pulido, Andrew I Cooper, Vitaliy Kurlin.
 Average Minimum Distances of periodic point sets  foundational invariants for mapping all periodic crystals.
 MATCH Communications in Mathematical and in Computer Chemistry, v.87(3), p.529559, 2022.

[31 pages, 2.6M]
[project page]
[reference]


 Aikaterini Vriza, Ioana Sovago, Dan Widdowson, Peter Wood, Vitaliy Kurlin, Matthew Dyer.
 Molecular Set Transformer: Attending to the cocrystals in the Cambridge Structural Database.
 Digital Discovery, v.1 (2022), p.834850.

[17 pages, 3.8M]
[project page]
[reference]


 Phil Smith, Vitaliy Kurlin.
 A practical algorithm for degreek Voronoi domains of threedimensional periodic point sets.
 Lecture Notes in Computer Science (Proceedings of ISVC 2022), v.13599, p.377391.

[14 pages, 2.1M]
[project page]
[reference]


 Olga Anosova, Vitaliy Kurlin.
 Density functions of periodic sequences.
 Lecture Notes in Computer Science (Proceedings of DGMM 2022: Discrete Geometry and Mathematical Morphology), v.13493, p.395408.

[13 pages, 2M]
[project page]
[reference]


 Jakob Ropers, Marco Mosca, Olga Anosova, Vitaliy Kurlin,
Andrew Cooper.
 Fast predictions of lattice energies by continuous isometry invariants of crystal structures.
 Proceedings of DAMDID : Data Analytics and Management in Data Intensive Domains, p.178–192.

[early version]
[project page]
[reference]


 Yury Elkin, Vitaliy Kurlin.
 Counterexamples expose gaps in the proof of time complexity for cover trees introduced in 2006.
 Proceedings of TopoInVis 2022 : IEEE Workshop on Topological Data Analysis and Visualization, p.917.

[9 pages, 240K]
[project page]
[reference]


 Grzegorz Muszynski, Vitaliy Kurlin, Dmitriy Morozov, Michael Wehner, Karthik Kashinath, Prabhat Ram
 Topological Methods for Pattern Detection in Climate Data.
 Big Data Analytics in Earth, Atmospheric and Ocean Sciences, p. 227242, Wiley.

[project page]
[reference]
[official link]

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 Yury Elkin, Vitaliy Kurlin.
 Isometry invariant shape recognition of projectively perturbed point clouds by the mergegram extending 0D persistence.
 Mathematics, 2021, 9(17), 2121.

[17 pages, 1.5M]
[project page]
[reference]


 Phil Smith, Vitaliy Kurlin.
 Skeletonisation algorithms with theoretical guarantees for unorganised point clouds with high levels of noise.
 Pattern Recognition, v.115 (2021), 107902.

[extended, 48 pages, 7.6M]
[project page]
[reference]


 Aikaterini Vriza, Angelos Canaj, Rebecca Vismara, Laurence Cook, Troy Manning, Michael Gaultois, Peter Wood, Vitaliy Kurlin, Neil Berry, Matthew Dyer and Matthew Rosseinsky.
 One class classification as a practical approach for accelerating ππ cocrystal discovery.
 Chemical Science, v.12 (2021), p.17021719.

[18 pages, 2.7M]
[project page]
[reference]


 G. Muszynski, Prabhat, J. Balewski, K. Kashinath, M. Wehner, V. Kurlin.
 Atmospheric Blocking Pattern Recognition in Global Climate Model Simulation Data.
 Proceedings of ICPR : International Conference on Pattern Recognition.

[8 pages, 5.9M]
[project page]
[reference]

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 Cameron Hargreaves, Matthew Dyer, Michael Gaultois, Vitaliy Kurlin, Matthew Rosseinsky.
 The Earth Mover’s Distance as a Metric for the Space of Inorganic Compositions.
 Chemistry of Materials, volume 32 (24), p.1061010620 (December 2020).

[11 pages, 3.5M]
[project page]
[reference]


 Arshad Siddiqui, Vitaliy Kurlin.
 Polygonal Meshes of Noisy Images based on a new Thinning Algorithm with Theoretical Guarantees.
 Proceedings of VISAPP 2020 (International Conference on Computer Vision Theory and Applications).

[10 pages, 16M]
[project page]
[reference]
[official link]


 Thomas Welsch, Vitaliy Kurlin.
 Synthesis through Unification Genetic Programming.
 Proceedings of GECCO : Genetic and Evolutionary Computation Conference.

[8 pages, 414K]
[official link]

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 Jonathan Rutz et al.
 The Atmospheric River Tracking Method Intercomparison Project (ARTMIP): Quantifying Uncertainties in Atmospheric River Climatology.
 Journal of Geophysical Research: Atmospheres, v. 124 (24), 2019, p. 1377713802.

[50 pages, 5.5M]
[project page]
[reference]


 Sara Kalisnik, Vitaliy Kurlin, Davorin Lesnik.
 A higherdimensional Homologically Persistent Skeleton.
 Advances in Applied Mathematics, v.102 (2019), p.113142.

[30 pages, 1M]
[project page]
[reference]


 Grzegorz Muszynski, Karthik Kashinath, Vitaliy Kurlin, Michael Wehner, Prabhat
 Topological Data Analysis and Machine Learning for Recognizing Atmospheric River Patterns in Large Climate Datasets.
 Geoscientific Model Development, v. 12, p. 613628, 2019.

[24 pages, 7.4M]
[project page]
[reference]
[official link]


 Naohiko Ban, Wataru Yamazaki, Vitaliy Kurlin.
 Development of a Reconstruction Method for Major Vortex Structure around Tandem Flapping Wing Object via Vortex Trajectory Method.
 American Institute of Aeronautics and Astronautics SciTech Forum (2019).

[37 pages, 7.2M]
[project page]
[reference]
[official link]


 Vitaliy Kurlin, Grzegorz Muszynski.
 A persistencebased approach to automatic detection of line segments in images.
 Proceedings of CTIC 2019 (Computational Topology in Image Context)
Lecture Notes in Computer Science, v. 11382 (2019), p. 137150.

[14 pages, 2.7M]
[project page]
[reference]
[official link]

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 Jonathan Rutz et al.
 The Atmospheric River Tracking Method Intercomparison Project (ARTMIP): project goals and experimental design.
 Geoscientific Model Development, v. 11, 24552474, 2018.

[20 pages, 5.3M]
[project page]
[reference]

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 Vitaliy Kurlin, Donald Harvey.
 Superpixels Optimized by Color and Shape (SOCS).
 Proceedings of EMMCVPR 2017 (Energy Minimization Methods in Computer Vision and Pattern Recognition), LNCS 10746, p. 297311, Springer.

[14 pages, 4.9M]
[project page]
[reference]

vs


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 Jeremy Forsythe, Vitaliy Kurlin,
Andrew Fitzgibbon.
 Resolutionindependent superpixels based on convex constrained meshes without small angles.
 Proceedings of ISVC 2016: International Symposium on Visual Computing.
 Lecture Notes in Computer Science, v. 10072, p. 223233.

[extended, 20 pages, 3.7M]
[project page]
[reference]


 Vitaliy Kurlin.
 A fast persistencebased segmentation of noisy 2D clouds with provable guarantees.
 Pattern Recognition Letters, v. 83 (2016), p. 312.

[full version: 16 pages, 4.2M]
[project page]
[reference]
[official]

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 Vitaliy Kurlin.
 A onedimensional Homologically Persistent Skeleton of a point cloud in any metric space.
 Computer Graphics Forum, v. 34, no. 5 (2015), p. 253262.
 A special issue devoted to SGP 2015:
Eurographics Symposium on Geometry Processing.

[extended, 14 pages, 3.2M]
[project page]
[reference]


 Vitaliy Kurlin.
 A Homologically Persistent Skeleton is a fast and robust descriptor of interest points in 2D images.
 Lecture Notes in Computer Science, v. 9256 (2015), p. 606617.
 (Proceedings of
CAIP 2015: Computer Analysis of Images and Patterns).

[12 pages, 1.2M]
[project page]
[reference]
[official link]


 Herbert Edelsbrunner, Mabel IglesiasHam, Vitaliy Kurlin.
 Relaxed disk packing.
 Proceedings of CCCG 2015:
Canadian Conference on Computational Geometry, p.128135.

[8 pages, 390K]
[project page]
[reference]


 Vitaliy Kurlin.
 A linear time algorithm for visualizing knotted structures in 3 pages.
 Proceedings of IVAPP 2015:
Information Visualization Theory and Applications, p. 516.

[12 pages, 2.5M]
[project page]
[reference]
[official link]

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 Vitaliy Kurlin.
 A fast and robust algorithm to count topologically persistent holes in noisy clouds.
 Proceedings of CVPR 2014:
Computer Vision and Pattern Recognition, p. 14581463
(top conference in Computer Science, the highest hindex conference in any field).

[extended: 10 pages, 1.6M]
[project page]
[reference]


 Vitaliy Kurlin.
 Autocompletion of contours in sketches, maps and sparse 2D images based on persistence.
 Proceedings of workshop CTIC (Computational Topology in Image Context) at SYNASC 2014
 (Symposium on Symbolic and Numeric Algorithms for Scientific Computing), p. 594601.

[8 pages, 1.1M]
[project page]
[reference]
[code: betaversion]


 Vitaliy Kurlin, Marjan SafiSamghabadi.
 Computing a skeleton of the configuration space of 2 round robots on a metric graph.
 Proceedings of ICRoM 2014:
International Conference on Robotics and Mechatronics, p. 723729.

[7 pages, 370K]
Slides [pdf, 32 pages, 1.6M]
[official link]

@inproceedings{kurlin2014computing,
author = {Kurlin, V. and SafiSamghabadi, M.},
title = {Computing a skeleton of the configuration space of 2 round robots on a metric graph},
booktitle = {Proceedings of ICRoM 2014: International Conference on Robotics and Mechatronics},
pages = {723729},
year = {2014}
}
 Input: a radius r of two robots and a metric graph G with fixed lengths of edges.
 Output: connected components of the configuration space of two robots in G.
 Running time: O(n^{4}) for the number n of vertices in the given graph G.
 Abstract. A connected metric graph G with n vertices and without loops and multiple edges can be represented as an nbyn matrix whose entries are length of edges of G. A robot in the metric graph G is a metric ball with a centre x in G and a radius r>0. The configuration space OC(G,r) of two robots in G is the set of all centers (x,y) such that the centres x,y are at least 2r away from each other. We introduce the configuration skeleton CS(G,r) that captures all connectivity information of the space OC(G,r). As a consequence we get a polynomial time algorithm to find all connected components of OC(G,r) that are maximal subsets of all positions (x,y) connectable by collisionfree motions.
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 Vitaliy Kurlin, Ludmila Mihaylova.
How many wireless sensors are needed to guarantee connectivity
of a 1D network with random internode spacings?
Journal of Applied Probability and Statistics,
v. 8 (2013), no. 2, p. 2750.
(1M, 24 pages).

Alexey Chernov, Vitaliy Kurlin.
Reconstructing persistent graph structures from noisy images.
Journal ImageA,
v. 3 (2013), no. 5, p. 1922.
(229K, 4 pages).
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 Vitaliy Kurlin.
Computing braid groups of graphs with applications to robot motion planning.
Homology, Homotopy and Applications,
v. 14 (2012), no. 1, p. 159180.
(249K, 22 pages).
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2008  2010 : singularity theory applied to knots and links
 Thomas Fiedler, Vitaliy Kurlin.
Recognizing trace graphs of closed braids.
Osaka Journal of Mathematics,
v. 47 (2010), no. 4, p. 885909.
(1.8M, 25 pages).
 Thomas Fiedler, Vitaliy Kurlin.
A oneparameter approach to links in a solid torus.
Journal of the Mathematical Society of Japan,
v. 62 (2010), no. 1, p. 167211.
(1.72M, 45 pages).
 Thomas Fiedler, Vitaliy Kurlin.
Fiber quadrisecants in knot isotopies.
J
Knot Theory Ramifications, v. 17 (2008), no. 11, p. 14151428.
(780K, 14 pages).
 Cherry Kearton, Vitaliy Kurlin.
All 2dimensional links live inside a universal 3dimensional polyhedron.
Algebraic & Geometric Topology, v. 8 (2008), no. 3, p. 12231247.
(560K, 25 pages).
 Vitaliy Kurlin.
Gauss paragraphs of classical links and a characterization of virtual link groups.
Math. Proc. Cambridge Phil. Society, v. 145 (2008), no. 1, p. 129140.
(223K, 12 pages).
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2005  2007 : postdoctoral work on noncommutative algebra
 Vitaliy Kurlin, Daniel Lines.
Peripherally specified homomorphs of link groups.
J Knot Theory Ramifications, v. 16 (2007), no. 6, p. 719740.
(435K, 22 pages).
 Vitaliy Kurlin.
The BakerCampbellHausdorff formula in the free metabelian Lie algebra.
Journal of Lie Theory, v. 17 (2007), no. 3, p. 525538.
(190K, 14 pages).
 Vitaliy Kurlin.
Threepage encoding and complexity theory for spatial graphs.
J Knot Theory Ramifications, v. 16 (2007), no. 1, p. 59102.
(800K, 44 pages).
 Vitaliy Kurlin.
Compressed Drinfeld associators.
Journal of Algebra, v. 292 (2005), no. 1, p. 184242.
(400M, 59 pages).
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2001  2004 : PhD work on classifications of embedded graphs
 Vitaliy Kurlin, Vladimir Vershinin.
Threepage embeddings of singular knots.
Functional Analysis and Its Applications, v. 38 (2004), no. 1, p. 1427.
(200K, 14 pages).
 Vitaliy Kurlin.
Basic embeddings and 3page embeddings of graphs.
Russian Mathematical Surveys, v. 58 (2003), no. 2, p. 372374.
(116K, 3 pages).
 Vitaliy Kurlin.
Threepage Dynnikov's diagrams of spatial 3valent graphs.
Functional Analysis and Its Applications, v. 35 (2001), no. 3, p. 230233.
(96K, 4 pages).
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1999  2000 : MSc work on link invariants and basic embeddings
 Vitaliy Kurlin.
Basic embeddings into a product of graphs.
Topology and Its Applications, v. 102 (2000), no. 2, p. 113137.
(225K, 25 pages).
 Vitaliy Kurlin.
Reduction of framed links to ordinary links.
Russian Mathematical Surveys, v. 54 (1999), no. 4, p. 845846.
(244K, 2 pages).
 Vitaliy Kurlin.
Invariants of colored links.
Moscow University Math. Bulletin, v. 54 (1999), no. 3, p. 4244.
(670K, 3 pages).
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Invited lectures at international conferences
2024 
2023 
2022 
20202021 
2019 
20172018 
2016 
2015 
20112014 
20072010 
20052006 
19992004
Videos of past talks, see also the most recent videos
 The Crystal Isometry Principle (13 min) at the
annual conference of the AI3SD network, Southampton, March 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 MS65 of the IUCr congress (online), August 2021.
 Introduction to invariantbased 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.
 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.
 Peristencebased 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.
 1min video spotlight
at CVPR 2014
(Computer Vision and Pattern Recognition), Columbus, Ohio (USA), June 2014.

Applications of Topological Data Analysis to Computer Vision (1 hour),
Microsoft
Research, Cambridge (UK), Feb 2014.

Reconstruction of plane graphs from noisy samples (1 hour),
Informatics Forum, Edinburgh University, April 2013.
Oral presentations in 2024
 September 2024 : Computational Persistence (ComPer), Graz, Austria
Title. Generic families of metric spaces with trivial 1D persistence (20 min).
 July 2024 : the minisymposium Geometric Data Science at the European Congress of Mathematics, Sevilla (Spain)
Title. Geographicstyle maps for moduli spaces of clouds of unordered points under rigid motion (30 min).
 June 2024 : Biomolecular Topology: Modelling and Data Analysis, Singapore
Title. Can we geometrically sense the shape of a molecule? (50min invited talk)
 May 2024 : the minisymposium at SIAM Mathematical Aspects of Materials Science, Pittsburgh (US)
Title. New mathematical principles in materials science (30 min).
 March 2024 : tutorial at the Materials Informatics workshop in IMSI, Chicago (US)
Title. A mathematical analysis of GNoME and other materials databases (60 min).
 March 2024 : the workshop Foundational Aspects of NeuroSymbolic Computing, Santiago (Chile)
Title. Introductory tutorial in Geometric Data Science (90 min).
 January 2024 :
Joint Mathematics Meetings, San Francisco (US)
 Title 1. Geometric Data Science: old challenges and new solutions
(AMS Special Session on Applied Topology: Theory, Algorithms, and Applications, 30 min)
 Title 2. The Crystal Isometry Principle
(SIAMUSNCTAM Minisymposium on Mathematical Modeling of Complex Materials Systems, 30 min)
 Title 3. A complete and continuous isometry invariant of Euclidean clouds of unordered points
(AMS Special Session on Mathematics of Computer Vision, 30 min)
 Title 4. Continuous maps of the highdimensional universe of protein structures
(AMS Special Session on Geometry and Topology of HighDimensional Biomedical Data, 25 min)
 Title 5. Continuous metrics on moduli spaces of lattices
(AMS Contributed Paper Session on Geometry, 15 min)
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Oral presentations in 2023
 August 2023 : International Union of Crystallography congress, Melbourne (Australia).
 Title 1. A continuous map of the Cambridge Structural Database in meaningful coordinates (30min invited talk).
 Title 2. The Crystal Isometry Principle justifies a new data standard for all periodic crystals (20min contributed talk).
 June 2023 : CVPR workshop TAGPRA: Topology, Algebra, and Geometry in Pattern Recognition, Vancouver (Canada).
Title : Recognizing rigid patterns of unlabeled point clouds by complete and continuous isometry invariants (1 hour).
 April 2023 : annual meeting of the British Crystallographic Association, University of Sheffield (United Kingdom)
Title : The Crystal Isometry Space continuously extends Mendeleev’s table to all periodic materials (20min talk).
 January 2023 : LMS workshop Applied topology and Robot Motion Planning, Queen Mary University of London, UK
Title : Geometric Data Science for unlabeled point clouds modulo Euclidean isometry (1hour invited talk)
 January 2023 : session `Topology, Algebra, and Geometry in the Mathematics of Data Science' at JMM, Boston (US)
Title : Geometric Data Science: old challenges and new solutions (30min talk).
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Oral presentations in 2022
 October 2022 : TopoInVis (Topological Data Analysis and Visualization) at IEEE VIS 2022, Oklahoma City (US)
Title : Counterexamples expose gaps in the proof of time complexity for cover trees introduced in 2006.
 October 2022 : Fall Workshop in Computational Geometry, North Carolina State University (US)
Title : Geometric Data Science challenges and solutions (20min talk).
 October 2022 : 17th International Symposium on Visual Computing, San Diego (US)
Title : A practical algorithm for degreek Voronoi domains of periodic point sets (20min talk).
 September 2022 : Topological Data Analysis and Machine Learning, online in Heidelberg (Germany)
Title : Generic families of finite sets with identical 1dimensional persistence (10min talk).
 September 2022 : The interdisciplinary world of tangling, Potsdam (Germany)
Title : Practical classifications of periodic structures require thinking outside the cell (30min talk).
 September 2022 : Maths and Computer Science for Materials Innovation (MACSMIN), Liverpool (UK)
Title : Geometric Data Science for continuous crystallography. Video (53 min).
 July 2022 : 32nd International Symposium on Chirality, Chicago (US)
Title : Easily computable chiral distances of 2D lattices (25min talk).
 July 2022 : Applied Topology in Frontier Sciences, online from Singapore
Title : Geometric Data Science challenges and solutions (50min invited talk).
 July 2022 : ICM geometry and topology section, Copenhagen (Denmark)
Title : Geometric Data Science challenges and solutions (15min talk).
 July 2022 : Applied Topology, Bedlewo Conference Centre (Poland)
Title : Geometric Data Science challenges and solutions (45min invited talk).
 June 2022 : annual workshop on Computational Topology at SoCG, Berlin (Germany)
Title : Persistence versus newer isometry invariants of point sets (30min invited talk).
 March 2022 : annual conference of the AI3SD network.
Title : The Crystal Isometry Principle (13min video).
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Oral presentations in 20202021
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Oral presentations in 2019
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Oral presentations in 20172018
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Oral presentations in 2016
 August 2016 : BTM 2016 (British Topology Meeting), Glasgow University (UK).
Title : Graph reconstruction from noisy scans based on persistence (1hour keynote lecture).
 July 2016 : ATMCS 8 (Applied Topology: Methods, Computation, Science), Turin (Italy).
Title : Graph reconstruction from noisy point samples (30min software demo).
 July 2016 : 7 ECM (European Congress of Mathematics), Berlin (Germany).
Title : Topological Computer Vision (20min contributed talk).
 April 2016 : symposium Today's Data Predicting Tomorrow, Loughborough (UK).
Title : Applications of Topological Data Analysis (25min invited talk).
 April 2016 : BAMC 2016: British Applied Mathematical Colloquium, Oxford (UK).
Title : Convex constrained meshes of superpixels (20min contributed talk).
 January 2016 : ATI workshop
Mathematical Foundations of Learning for nonEuclidean Objects, London (UK).
Title : Topological Computer Vision (20min invited talk).
 January 2016 : Prospects in Data Science, Southampton (UK).
Title : Topological Computer Vision (40min keynote lecture).
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Oral presentations in 2015
 October 2015 :
Computational Geometric and Algebraic Topology, Oberwolfach (Germany).
Title : HoPeS (cloud segmentations and persistent skeletons): (15min software demo).
 September 2015 :
CAT 2015:
Computational Algebraic Topology, Oxford (UK).
Title : Topological Computer Vision is a new area in Topological Data Analysis (25min invited talk).
 July 2015 :
ACA 2015:
Applications of Computer Algebra, Kalamata (Greece).
Title : Fast and stable topological profiles of noisy 2D images (30min contributed talk).
 July 2015 :
ACAT 2015:
Applied and Computational Algebraic Topology, IST Austria.
Title : A homologically persistent skeleton of an unstructured point cloud (40min contributed talk).
 July 2015 :
SGP 2015:
Eurographics Symposium on Geometry Processing, Graz (Austria).
Title : A homologically persistent skeleton of an unstructured point cloud (30min talk with the accepted paper).
 June 2015 :
DyToComp 2015:
Dynamics, Topology, and Computation, Bedlewo (Poland).
Title : A Homologically Persistent Skeleton in Computer Vision and beyond (30min contributed talk).
 May 2015 :
MMMDS:
Mathematical Methods for Massive Data Sets, Edinburgh (UK).
Title : Topological Data Analysis. Applications to Computer Vision (45min invited talk).
 May 2015 :
TopoInVis 2015:
TopologyBased Methods in Visualization, Annweiler (Germany).
Title : Computing invariants of knotted graphs given by sequences of 3D points (25min talk with the accepted paper).
 April 2015 :
BAMC:
British Applied Mathematical Colloquium, Cambridge (UK).
Title : Topological Data Analysis. Applications to Computer Vision (20min contributed talk).
 March 2015 :
IVAPP:
Information Visualization Theory and Applications, Berlin (Germany).
Title : A linear time algorithm for visualizing knotted structures in 3 pages (30min talk with the accepted paper).
 February 2015 :
Algebraic Topology: Computation, Data Analysis, and Applications
workshop at the Oxford Mathematical Institute (United Kingdom).
Title : Homologically persistent skeleton (20min invited talk).
 January 2015 :
Applied
Algebraic Topology network, Queen Mary University of London (UK).
Title : Topological Data Analysis. Applications to Computer Vision (45min invited talk).
 January 2015 :
Transpennine
Topology Triangle meeting, University of Sheffield (UK).
Title : Topological Data Analysis. Applications to Computer Vision (1 hour).
 January 2015 : Winter School on Lowdimensional Topology, La Llagonne (France).
Title : Topological Data Analysis. Applications to Computer Vision (45min invited talk).
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Oral presentations in 20112014
 September 2014 :
CTIC: Computational Topology in Image Context, Timisoara (Romania).
 Title 1 : Autocompletion of closed contours based on topological persistence (20 min).
 Title 2 : Drawing a graph in 3 pages within its isotopy class in a linear time (20 min).
 September 2014 :
British Topology Meeting,
Southampton (United Kingdom).
Title : Topological Data Analysis. Applications to Computer Vision (30 min).
 July 2014 :
Applied Algebraic Topology,
CIEM, Castro Urdiales (Spain).
Title : Homologically Persistent Skeleton for visualizing highdimensional data (45 min).
 July 2013,
Applied Topology,
Bedlewo Conference Centre (Poland).
Title : Reconstructing persistent structures from
noisy images of graphs in a metric space (40 min).
 July 2013 :
Applied
and Computational Algebraic Topology, Bremen (Germany).
Title : Persistent homotopy types of noisy samples of graphs in the plane (30 min).
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Oral presentations in 20072010
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Oral presentations in 20052006
 September 2006 :
Lowdimensional Manifolds,
Burgo de Osma (Spain).
Title : Compressed Drinfeld associators (25 min).
 August 2006 :
International
Congress of Mathematicians 2006,
Madrid (Spain).
Title : Compressed BakerCampbellHausdorff formula
(20min oral communication).
 May 2006 :
Knots,
Groups and 3Manifolds,
Marseille (France).
Title : Peripherally specified homomorphs of link groups (20 min).
 April 2006 :
54th
Transpennine Topology Triangle meeting,
Sheffield (UK).
Title : Compressed BakerCampbellHausdorff formula (1 hour).
 April 2006 :
Algebraic Geometry,
Singularities, Knots,
Liverpool (UK).
Title : Topological approach to the conjugacy of braids (1 hour).
 April 2006 :
British Mathematical Colloquium 2006,
Newcastle (UK).
Title : Compressed BakerCampbellHausdorff formula (25 min).
 November 2005 :
Combinatorial Braid Theory, Brighton (UK).
Title : Oneparameter approach to knot theory (45+45 min).
 June 2005, Rencontres du GDR Tresses (braids), Luminy (France).
Title : Fiedler's 1parameter approach to knot theory (30 min).
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Oral presentations in 19992004
 September 2004 :
Rencontres du GDR Tresses (braids), Tatihou (France).
Title : Description of compressed Drinfeld associators (40 min).
 July 2004 :
Geometry, Topology and Combinatorics (satellite of
ECM 2004), Stockholm (Sweden).
Title : Computing compressed Drinfeld associators (30 min).
 June 2004 : Rencontres du GDR Tresses (braids), Autrans (France).
Title : A program to compute Drinfeld associators (30 min).
 May 2003 : Kolmogorov and Contemporary Mathematics, Moscow.
Title : Basic embeddings of graphs (20 min).
 June 2001 : Knot Theory and Algebraic Geometry, Liverpool (UK).
Title : Threepage embeddings of spatial 3valent graphs (30 min).
 October 2000 :
Combinatorcs, Dynamics and Probability, Stockholm (Sweden).
Title : Algebraic classification of spatial 3valent graphs (30 min).
 March 2000 :
Geometry and Applications,
Novosibirsk.
Title : Diagrams of spatial 3valent graphs (20 min).
 August 1999 : Lowdimensional topology and combinatorial group theory,
Chelyabinsk.
Title : Reduction of framed links to ordinary ones (30 min).
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Smaller research grants, see also larger awards

Faculty summer bursaries (value 2×1K GBP) at the University of Liverpool for 2nd year undergraduates Cristian Badoi and Wenkai Zhang (2019). 

Since 2017 the organiser of the network Applied Geometry and Topology covering 3 meetings per year at the Universities of Liverpool, Queen Mary (G.Bianconi, M.Farber) and Southampton (J.Brodzki, J.Grbić), funded by the London Mathematical Society (total value 7.2K GBP in 20172022).


EPSRC vacation bursaries (value 2×2.7K GBP) at the University of Liverpool for 2nd year undergraduates Simon Hirst (2017) and Gee Jack (2018). 

Summer bursary of the London Mathematical Society for Philip Smith (value 1.1K GBP)
to work on the project Superpixel meshes for faster image and video processing in August  September 2016, closely related to the collaboration with
Microsoft Research Cambridge. 

Christopherson/Knott fellowship at
Institute of Advanced Study (left after moving to Liverpool, UK). Title : Optimal meshes of superpixels for faster image processing (7.5K GBP 3month teaching replacement). 

Conference grant (3K GBP, jointly with M.Grinfeld and
M.Haw) to run the ATI strategic workshop on 14 March 2016 : Topological Data Analysis in Materials Science and Engineering. 

Travel grant of the London Mathematical Society to give the contributed 20min talk
Topological Computer Vision in the section Mathematical Image and Signal Processing at 7ECM (European Congress of Mathematicians) at
TU Berlin on 1822 July 2016. 

Travel grant (1.7K Euros) by the ACAT
(Applied and Computational Algebraic Topology) network of ESF (European Science Foundation) to visit IST Austria (March 2015). 

INTAS
PhD Fellowship (10K Euros) at
Moscow State University,
March 2001  February 2003, covered research collaboration at
Universities of Montpellier II, Liverpool, Dijon, Toulouse III, Paris VII. 
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Coauthors in the alphabetical order (last updated in 2016)
 Alexey Chernov : Senior Lecturer in Statistics at University of Brighton, UK
 Herbert Edelsbrunner : Professor at IST Austria
 Thomas Fiedler : Professor at University of Toulouse III, France
 Andrew Fitzgibbon: Principal Researcher at Microsoft Research Cambridge, UK
 Jeremy Forsythe : former final year project student, UK
 Donald Harvey : former final year project student, UK
 Mabel IglesiasHam : PhD graduate from IST Austria
 Cherry Kearton : retired Reader, UK
 Daniel Lines : retired Professor at University of Burgundy, Dijon, France
 Ludmila Mihaylova : Professor at University of Sheffield, UK
 Marjan SafiSamghabadi :
Lecturer at International Imam Khomeini University, Iran
 Christopher Smithers : former PhD student, UK
 Vladimir Vershinin : Professor at University of Montpellier II, France
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