I'm looking for motivated MSc/PhD students and postdocs with C++ or Python skills to work on exciting projects in Topological Data Analysis with applications to Materials Science, Computer Vision, Climate System.
Please email vitaliy.kurlin(at)gmail.com if you are interested and would like to join the group in Topological Data Analysis.

Potential projects for PhD, MSc and undergraduates: join us
 The projects are for students of the University of Liverpool from summer 2018, but can be considered by external interns.
 Project :
Visualising shapes of highdimensional datasets.
Description. The aim is to build an interactive software tool for visualising complicated datasets where each data point has many coordinates (features or descriptors). If we fix a suitable similarity measure (a distance function) between data points, we can split a given dataset into groups (clusters) consisting of similar data points. Depending on a threshold for clustering, the clusters can be interlinked into interesting patterns. For example, the shape of a dataset may look like a circular chain of clusters or can have a more complicated branched pattern. Our main data will be the CSD (Cambridge Structural Database) containing over 900K crystal structures. These structures represent solid materials with useful chemical properties. The big problem is to find better materials with desired properties such as superconductivity or capacity for storing gases (methane or carbon dioxide). Each crystal structure consists of several atoms given by their geometric positions in a unit cell (a nonrectangular box). After translating this box in 3 directions, the initial arrangement of atoms becomes an infinite periodic crystal structure in 3D. The selected student might have a desk in the Materials Innovation Factory and can be advised by colleagues working in Computational Chemistry and in the CCDC (Cambridge Crystallographic Data Centre). The CCDC maintains the widelyused software Mercury, which visualises crystal structures only individually and can compare them only pairwisely. Hence a new tool visualising the entire CSD can have a big commercial impact. An ideal candidate will have strong programming skills, preferably in C++. The implementation will use the software libraries Boost Graph and OpenCV. This research can be continued as a final year Computer Science project from October 2018. In addition, depending on the overall success, there is an excellent chance to continue working in the same direction as a PhD student funded from October 2019.  Project :
Classifying periodic knotted structures.
Description. The big aim is to design new algorithms for classifying periodic entanglements consisting of knotted strands. These structures appear in physical simulations and theoretical models of new materials. The current final year project student has made a good progress in the 2periodic case when such knotted structures are represented by diagrams with crossings in a plane square. The classical case of the encoding problem for classical knots and links (closed loops in 3space without periodicity) was solved by Dr Vitaliy Kurlin in 2008. The first step in the project is to encode diagrams of knotted structures with a triple symmetry, which can be visualised as closed loops in 3D torus (a product of 3 circles or a solid cube whose 3 pairs of opposite faces are glued together). The selected student might have a desk in the Materials Innovation Factory and should have strong programming skills in C++. The project will use the libraries Boost Graph and OpenCV. This research can be continued as a final year Computer Science project from October 2018.  Project :
Image processing for physical simulations.
Description. The aim is to implement an automatic software tool to recognise geometric patterns in large microscopic images of physical simulations. The images contain patterns of socalled vortices and antivortices connected by curved arcs that split an image into curved polygons. Physics colleagues currently use highschool students for manually counting vertices and edges of polygons. There is already a good initial code that automatically detects polygonal regions. These regions are now separated by straight rectangular blocks that should be further thinned to identify positions of vertices and edges between polygons. The selected student might have a desk in the Materials Innovation Factory and will gain Computer Vision skills that will be helpful in the computer games industry. On the academic side, depending on a success of the project, the student can become coauthor in a highprofile interdisciplinary publication and will have excellent prospects in gaining a funded PhD studentship at a top university. An ideal candidate will have strong programming skills, preferably in C++. The implementation will use the software libraries Boost Graph and OpenCV. This research can be continued as a final year Computer Science project from October 2018.
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Past members of the Topological Data Analysis group
 Dr Alexey Chernov : postdoc in 2011  2012, now a Senior Lecturer in Statistics at Brighton University, we continue our collaboration on combining Topological Data Analysis with Machine Learning.
 Dr Marjan SafiSamghabadi : PhD student in 2009  2013, a lecturer at International Imam Khomeini University, Iran.
 Shortterm project students in 201718 (various periods from 8 weeks to 8 months): Abid Abdul (2nd year), Alex Bagnall (3rd year), Naohiko Ban (visiting PhD), Jacob Bracken (3rd year), Matthew Bright (MSc), Gemma Cook (MSc), Cameron Hargreaves (MSc), Di Liu (2nd year), Jingyi Lu (3rd year), Asim Munshi (graduate intern), Andrew Parry (3rd year), Antoine Rohmer (2nd year), Arshad Siddiqui (selffunded intern), Eris Tricker (graduate intern), Thomas Welsch (MSc).
 Summer students in 2017 : Graham Briggs (MSc), Jason Brewer (MSc), Sandra Garcia (MSc), Yuyao Wang (MSc), Zijian Li (MSc), Simon Hirst (EPSRC), Aviral Srivastava (selffunded intern), Falgun Patel (selffunded intern).
 Mr Christopher Smithers : PhD supervised in 20152016 before moving to Liverpool, funded by the Leverhulme Trust.
 Summer students in 2016 : David Torkington (MSc), Cheng Shen (MSc), Phil Smith (LMS), Aryaman Patel (intern on site).
Past student projects and highlighted achievements
 PhD student Ms Marjan SafiSamghabadi (selffunded) has successfully completed her MSc and PhD in Topological Robotics under my supervision in June 2009  June 2013. Here is the joint paper based on her PhD.
 Year 4 student Donald Harvey has completed in 2016 the brilliant project Coarsetofine superpixel segmentation with a fast adaptive energybased initialisation leading to the joint paper Superpixels Optimized by Color and Shape.
 Year 4 student Jeremy Forsythe has completed in 2016 the excellent project Convex Constrained Meshes: a new method to generate resolutionindependent superpixels leading to the joint paper with Microsoft, see the journal version.
 The projects of Mr Caspar De Haes (Map Colouring), Mr Chris Palmer (Topological Robotics) were ranked the 2nd and 4th best year 4 projects in the department in 2011.
 MSc dissertations (3 months in the summer):
 Mr Cheng Shen: Data Skeletonization via alphaReeb Graphs (2016)
 Mr David Torkington: Testing the Mapper skeletonisation algorithm (2016)
 Mr Christopher Smithers: A linear time algorithm for embedding arbitrary knotted graphs into a 3page book (2015)
 Ms Marjan SafiSamghabadi: Configuration Spaces of Graphs (2009)
 Mrs Suad Alkhmas: Virtual Knots and Knotted Graphs (2008)
 Topological Data Analysis : all other projects
 Mr Christopher Parkinson: Klein bottle model for a cloud of small patches from colour images (2016, year 4)
 Mr Lewin Strauss: The skeletonisation problem in high dimensions (2016, year 4)
 Topological Robotics : all other projects
 Mr Sam Bullen: Topological Complexity of Robot Motion Planning (2013, year 4)
 Ms Alison Champernowne: Straightening a Robot Arm in the Plane (2013, year 4)
 Mr Nathan Edwards: Euler Characteristic of Configuration Spaces (2013, year 4)
 Mr Chris Guard: Locked Polygonal Linkages in 3dimensional Space (2013, year 4)
 Mr Martin Smith: Homotopy Types of Configuration Spaces of Graphs (2012, year 4)
 Ms Emily Weir: Connectivity Algorithms for Configuration Spaces (2012, year 4)
 Mr Chris Walker: Topological Complexity of Configuration Spaces (2011, year 4).
 Map Colouring : all other projects
 Ms Katriina Nichols (2010, year 4)
 Ms Camilla Banks (2009, year 3).
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Links to useful resources for completing projects
 LaTeX Wikibook, LaTeX tutorials by Andrew Roberts.
 Graphics program: Inkscape available for free.
 Free tutorials on HTML by W3Schools.
 Free tutorials on Java by Oracle.
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