
Selected papers in top journals and conferences
 This paper has received the highest praise from numerous colleagues.
V. Kurlin, A fast persistencebased segmentation of noisy 2D clouds with provable guarantees,
PRL : Pattern Recognition Letters, v. 83 (2016), p. 312.  This paper introduces HoPeS, my key contribution to Topological Data Analysis.
V. Kurlin, A onedimensional Homologically Persistent Skeleton of an unstructured point cloud in any metric space,
CGF : Computer Graphics Forum, v. 34, no. 5 (2015), p. 253262.  Published in the top 3 conference in Computer Science, the highest hindex conference in any field.
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 is the highest cited paper, where I was the leading author (the second alphabetically).
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 is my most substantial 59page paper in pure mathematics.
V. Kurlin, Compressed Drinfeld associators, Journal of Algebra, v. 292 (2005), no. 1, p. 184242.  This paper was completed during the 2nd year of the undergraduate degree.
V. Kurlin, Basic embeddings into a product of graphs, Topology and Its Applications, v. 102 (2000), no. 2, p. 113137.
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All papers by research topics and chronologically (Google scholar)
 Applied Mathematics (Topological Data Analysis for applications)
 Atmospheric Rivers (Climate Science) : GMD 2019  GMD 2018  CI 2018
 Persistent skeletons (Topological Data Analysis) : AAM 2019  CGF 2015  CAIP 2015  ImageA 2013
 Polygonal meshes (Computer Vision): CTIC 2019  EMMCVPR 2017  JEI 2017  ISVC 2016
 Point cloud analysis (Topological Data Analysis) : PRL 2016  CVPR 2014  CTIC 2014
 Knotted graphs (Materials Science) : MathVis 2017  CCIS 2016  IVAPP 2015
 Probabilistic networks : CCCG 2015  JAPS 2013
 Topological robotics : ICRoM 2014  HHA 2012
 Pure mathematics (graphs, topology and noncommutative Algebra):
 2008  2010 : singularity theory related to knots and links
 2005  2007 : postdoctoral work on noncommutative algebra
 2001  2004 : PhD work on 3page embeddings of graphs
 1999  2000 : MSc work on link invariants and basic embeddings
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2019 : AAM GMD CTIC


@article{muszynski2019topological, title={Topological Data Analysis and Machine Learning for Recognizing Atmospheric River Patterns in Large Climate Datasets}, author={Grzegorz Muszynski and Karthik Kashinath and Vitaliy Kurlin and Michael Wehner and Prabhat}, journal={Geoscientific Model Development}, volume={12}, year={2019} }
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2018 : GMD CI

@article{shields2018atmospheric, title={Atmospheric River Tracking Method Intercomparison Project (ARTMIP): project goals and experimental design}, author={Shields, Christine and Rutz, Jonathan and Leung, LaiYung and Ralph Martin and Wehner, Michael and others}, journal={Geoscientific Model Development}, volume={11}, number={6}, pages={24552474}, year={2018} }

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2017 : EMMCVPR JEI MathVis

vs 


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2016 : ISVC PRL CCIS



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2015 : CGF CAIP CCCG IVAPP



@inproceedings{EIHK15CCCG, author = {Edelsbrunner, E. and IglesiasHam, M. and Kurlin, V.}, title = {Relaxed disk packing}, booktitle = {Proceedings of CCCG 2015: Canadian Conference on Computational Geometry}, year = {2015} }

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2014 : CVPR CTIC ICRoM
 


@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 2 robots and a metric graph G with fixed lengths of edges.
 Output: connected components of the configuration space of 2 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 2 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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2013 : JAPS ImageA
 Vitaliy Kurlin, Ludmila Mihaylova.
How many wireless sensors are needed to guarantee connectivity of a 1dimensional network with random internode spacings?
J Applied Probability and Statistics, v. 8 (2013), no. 2, p. 2750.
(223K, 24 pages). 
Alexey Chernov, Vitaliy Kurlin.
Reconstructing persistent graph structures from noisy images.
ImageA, v. 3 (2013), no. 5, p. 1922.
(234K, 4 pages).
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2012 : HHA
 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 : earlier work in pure mathematics
 Thomas Fiedler, Vitaliy Kurlin.
Recognizing trace graphs of closed braids.
Osaka J Mathematics, v. 47 (2010), no. 4, p. 885909.
(1M, 25 pages).  Thomas Fiedler, Vitaliy Kurlin.
A oneparameter approach to links in a solid torus.
J Math Society of Japan, v. 62 (2010), no. 1, p. 167211.
(1.5M, 45 pages).  Thomas Fiedler, Vitaliy Kurlin.
Fiber quadrisecants in knot isotopies.
J Knot Theory Ramifications, v. 17 (2008), no. 11, p. 14151428.
(846K, 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.
(913K, 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.
(212K, 12 pages).
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2005  2007 : postdoctoral work
 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.
(192K, 14 pages).  Vitaliy Kurlin.
Threepage encoding and complexity theory for spatial graphs.
J Knot Theory Ramifications, v. 16 (2007), no. 1, p. 59102.
(786K, 44 pages).  Vitaliy Kurlin.
Compressed Drinfeld associators.
Journal of Algebra, v. 292 (2005), no. 1, p. 184242.
(1.3M, 59 pages).
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2001  2004 : PhD studies
 Vitaliy Kurlin, Vladimir Vershinin.
Threepage embeddings of singular knots.
Functional Analysis and Its Applications, v. 38 (2004), no. 1, p. 1427.
(212K, 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.
(107K, 4 pages).
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1999  2000 : MSc studies
 Vitaliy Kurlin.
Basic embeddings into a product of graphs.
Topology and Its Applications, v. 102 (2000), no. 2, p. 113137.
(273K, 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.
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Invited lectures at international conferences
20172018  2016  2015  20112014  20072010  20052006  19992004
Oral presentations given in 20172018
 November 2018 : the workshop Trends in Persistent Homology in Queen's University Belfast (UK).
Title : "A comparison of skeletonization algorithms for unorganized point clouds" (50min invited talk).  June 2018 : Data Science summer school, Ecole Polytechnique near Paris (France).
Title : Topological Data Analysis (6hour tutorial with demonstrations in Python).  June 2018 : SIAM Imaging Sciences, University of Bologna (the oldest in the world), Italy
Title : "Superpixels for image oversegmentation based on topological skeletons" (30min invited talk).  September 2017 : Mathematical Signal Processing and Data Analysis, Bremen (Germany).
Title : "Topological methods for a faster materials discovery" (30min contributed talk).  June 2017 : Applied Topology,
Bedlewo Conference Centre, Poland.
Title : "Topological methods for a faster materials discovery" (45min invited talk).  May 2017 : International workshop on machine learning and data analytics in advanced metals processing, Manchester.
Title : "Topological Data Analysis for Materials Science" (30min contributed talk).  May 2017 : ACAT
(Applied and Computational Algebraic Topology), HIM Bonn, Germany.
Title : "Line segment detector inspired by Topological Data Analysis" (20min software demo).
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Oral presentations given 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, 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 given 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 given 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 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 given in 20072010
 June 2010,
Applied Topology:
Methods, Computation, Science, Munster, Germany.
Title : Braid groups of graphs and robot motion planning (30 min).  September 2009,
8th
Mathematics of Networks meeting, Cambridge, UK.
Title : Connectivity of random 1dimensional networks (45 min).  July 2009,
de
Brun Workshop on Computational Algebra, Galway, Ireland.
Title : The metabelian BCH formula and Drinfeld associators (45 min).  June 2008,
Differential Equations and Topology,
Moscow, Russia.
Title : Peripherally specified homomorphs of link groups (20 min).  April 2007,
British
Mathematical Colloquium 2007, Swansea, UK.
Title : Basic embeddings of graphs (20 min).
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Oral presentations given 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 given 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, Russia.
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, Russia.
Title : Diagrams of spatial 3valent graphs (20 min).  August 1999, Lowdimensional topology and combinatorial group theory,
Chelyabinsk, Russia.
Title : Reduction of framed links to ordinary ones (30 min).
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Seminar of the Topological Data Analysis group
The seminar is on Fridays between 13.0015.00 in the 3rd floor meeting room of the MIF : 201819  201718
Group seminars in the academic year 20182019
 25 January 2019. Ana Garcia. Simplicial complexes and homology groups.
 18 January 2019. Grzegorz Muszynski. Support Vector Machine and tDistributed Stochastic Neighbor Embedding.
 11 January 2019. Grzegorz Muszynski. Topological & Machine Learning Pattern Detection Methods in Climate Data.
 14 December 2018. Phil Smith. Skeletonisation algorithms for unstructured point clouds with theoretical guarantees.
 7 December 2018. Yury Elkin. Dualtree algorithms and applications to data skeletonization.
 30 November 2018. Fraser Holloway. A classification of pulse shapes from AGATA.
 23 November 2018. Miloslav Torda. Optimal lattice packings in Euclidean spaces.
 16 November 2018. Ana Garcia. Homotopy equivalence and simplicial complexes.
 9 November 2018. Katerina Vriza. Symmetry groups of crystals in dimensions 2 and 3.
 2 November 2018. Arshad Siddiqui. Polygonal vortex meshes in microscopic images.
 26 October 2018. Cameron Hargreaves. Crystal lattices and notations for space groups.
 19 October 2018. Thomas Welsch. Helping a robot to see a correctly placed piece of cloth.
 12 October 2018. Krasen Samardzhiev. A Pythonbased tutorial on alphacomplexes.
 5 October 2018. Krasen Samardzhiev. A Pythonbased tutorial on Delaunay triangulations.
 28 September 2018. Marco Mosca. Voronoi diagrams and Delaunay triangulations.
 24 September 2018. Ana Garcia. Combinatorial and topological graphs and their invariants.
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Group seminars in the academic year 20172018
 14 June 2018. Krasen Samardzhiev. A Pythonbased tutorial on Topological Data Analysis.
 31 May 2018. Grzegorz Muszynski. Diffusion maps for dimensionality reduction with examples.
 24 May 2018. Grzegorz Muszynski. Finding periodic behaviour in lowdimensional representations of climate data.
 10 May 2018. Krasen Samardzhiev. 1D persistent homology of census data in the US.
 3 May 2018. Phil Smith. Reeb graphs and alphaReeb graphs for data skeletonisation.
 26 April 2018. Phil Smith. Duality between persistent homology in dimensions 0 and 1 for 2D clouds.
 12 April 2018. Krasen Samardzhiev. Persistent homology of alphacomplexes for 2D clouds.
 22 March 2018. Krasen Samardzhiev. Homology groups: matrix computations.
 15 March 2018. Krasen Samardzhiev. Homology groups: manual computations.
 8 March 2018. Yury Elkin. Data skeletonisation algorithms for unorganised point clouds.
 22 February 2018. Naohiko Ban. Reconstruction of a vortex structure from 2D sequential images.
 15 February 2018. Eris Tricker. Converting pixelbased skeletons into planar graphs.
 8 February 2018. Asim Munshi. Thinning algorithms for blackandwhite images.
 25 January 2018. Grzegorz Muszynski. A topological detection of Atmospheric Rivers.
 18 January 2018. Krasen Samardzhiev. Kuratowski's criterion for planar graphs.
 11 January 2018. Yury Elkin. Straightening algorithms for polygonal curves.
 20 December 2017. Yury Elkin. Skeletons of 3D clouds from micelles.
 14 December 2017. Fraser Holloway. Pulse shapes from AGATA.
 7 December 2017. Graham Briggs. Periodic crystal structures.
 30 November 2017. Phil Smith. Simplest polygonal surfaces.
 23 November 2017. Yury Elkin. The Euler characteristic.
 16 November 2017. Krasen Samardzhiev. The unionfind algorithm.
 9 November 2017. Krasen Samardzhiev. Clustering algorithms for point clouds.
 2 November 2017. Phil Smith. Topological equivalences of graphs.
 17 October 2017. Phil Smith. Combinatorial graphs.
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Smaller research grants, see also larger awards
Since 2017 the organiser of the network Applied Algebraic Topology covering 3 meetings per year at the Universities of Liverpool (with Dr Ana Garcia), Queen Mary (G.Bianconi, M.Farber) and Southampton (J.Brodzki, J.GrbiÄ‡), funded by the London Mathematical Society (value about 4.2K GBP since 2017).  
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 (Russia), 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
 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 in the UK
 Donald Harvey : former final year project student in the UK
 Mabel IglesiasHam : PhD graduate from IST Austria
 Cherry Kearton : retired Reader in the 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 in the UK
 Vladimir Vershinin : Professor at University of Montpellier II, France
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