Applied Algebraic Topology (AAT) network in the UK

Next meeting of the Applied Algebraic Topology network
 Because of COVID19 meetings of the AAT network will hopefully continue online in 2021.
 In November 2019 the London Mathematical Society has extended the funding for another year until September 2020.
 If you would like to offer a talk at the next AAT meeting, please email the title and abstract to one of local organisers.
 The London Mathematical Society partially covers local travel and accommodation of participants of the AAT meetings.
Organisers of the Applied Algebraic Topology network
 Prof Ginestra Bianconi (ginestra.bianconi at gmail.com), Queen Mary University of London
 Prof Jacek Brodzki (j.brodzki at soton.ac.uk), University of Southampton
 Prof Michael Farber (m.farber at qmul.ac.uk), Queen Mary University of London
 Prof Jelena Grbic (j.grbic at soton.ac.uk), University of Southampton
 Dr Vitaliy Kurlin (vitaliy.kurlin at gmail.com), University of Liverpool.
Past meetings of the Applied Algebraic Topology network
2020 : Liverpool (joint with the MACSMIN conference)
2019 : ATI London  Liverpool  Queen Mary London
2018 : Liverpool  Southampton  Queen Mary London
 The 14th meeting was joint with the workshop Mathematics and Data organised by Prof Michael Farber (Queen Mary) at the Alan Turing Institute on 12th September 2019 in London, UK.
 10:30 – 10:35 Introduction and welcome – Michael Farber (The Alan Turing Institute)
 10:35 – 11:20 Expander graphs  Nati Linial (Hebrew University of Jerusalem
 11:20 – 12:05 Local view of combinatorial structures and applications to data analysis – Chaim EvenZohar (The Alan Turing Institute)
 12:05 – 12:50 On the expressiveness of comparison queries – Shay Moran (Princeton University)
 13:45 – 14:30 Topological complexity and its applications – John Oprea (Cleveland State University)
 14:30 – 15:15 Classical information theory of networks – Ginestra Bianconi (Queen Mary University of London and The Alan Turing Institute)
 15:30 – 16:15 An introduction to tropical geometry and connections to deep learning – Felipe Rincon (Queen Mary University of London)
 16:15 – 17:00 The simplicity revolutions in the era of complexity and the unreasonable effectiveness of small neural ensembles in highdimensional brain – Alexander Gorban (University of Leicester)
 The 13th meeting on Friday 30th August 2019 was organised by Dr Vitaliy Kurlin in the Materials Innovation Factory.
 9.3010.30 Prof Herbert Edelsbrunner (IST Austria)
Title. Tripartition of and hole systems in a polyhedral complex
Abstract. We prove that for every polyhedral complex, K, and every dimension, p, there is a partition of the pcells into a maximal ptree, a maximal pcotree, and the remaining pcells defining the pth homology of K. As an application, we consider the manipulation of the hole structure in geometric shapes, using the tripartition to facilitate the opening and closing of holes. In a concrete application, we let K be the Delaunay mosaic of a finite set, and we extract a partial order on the filtration induced by the radius function, whose cuts define the subcomplexes that can be constructed with this method. Joint work with Katharina Oelsboeck.  11.0012.00 Dr
Argyrios Deligkas (MIF, Liverpool)
Title. Crystal Structure Prediction via Oblivious Local Search
Abstract. We study Crystal Structure Prediction, one of the major problems in computational chemistry. This is essentially a continuous optimization problem, where many different, simple and sophisticated, methods have been proposed and applied. The simple searching techniques are easy to understand, usually easy to implement, but they can be slow in practice. On the other hand, the more sophisticated approaches perform well in general, however almost all of them have a large number of parameters that require fine tuning and, in the majority of the cases, chemical expertise is needed in order to properly set them up. In addition, due to the chemical expertise involved in the parametertuning, these approaches can be biased towards previouslyknown crystal structures. Our contribution is twofold. Firstly, we formalize the Crystal Structure Prediction problem, alongside several other intermediate problems, from a theoretical computer science perspective. Secondly, we propose an oblivious algorithm for Crystal Structure Prediction that is based on local search. Oblivious means that our algorithm requires minimal knowledge about the composition we are trying to compute a crystal structure for. In addition, our algorithm can be used as an intermediate step by {\em any} method. Our experiments show that our algorithms outperform the naive basin hopping, a standard, well studied, algorithm for the problem. Joint work with Dmytro Antypov, Vladimir Gusev, Matthew J. Rosseinsky, Paul G. Spirakis, Michael Theofilatos.  14.0015.00 Mr Georg Osang (IST Austria)
Title. The Multicover Persistence of Euclidean Balls
Abstract. Persistent homology has become a popular tool to analyse various kinds of data, in particular in material sciences. Specifically, persistence of discrete point sets has recently been used to analyse sphere packing data, to shed light on structures arising in sphere packings at different packing densities. We generalize this notion and introduce higherorder persistence of discrete point sets. We address computational challenges and show how this notion can deal with noisy point samples. In the setting of sphere packings we show that this notion can also capture a wider variety of local structures, and in particular can distinguish between the hexagonal close packing and the face centered cubic lattice packing, two structures know to have optimal packing density in 3 dimensions.  15.1016.10 Ms Teresa Heiss (IST Austria)
Title. A topological approach to comparing crystals (periodic point sets)
Abstract. As the atoms in crystals are arranged periodically, crystalline materials can be modeled by periodic point sets. Two periodic point sets are considered equivalent if there is a rigid motion from one to the other. A periodic point set can be represented by a finite cutout s.t. copying this cutout in all directions yields the periodic point set. As these cutouts are not unique, comparing periodic point sets for similarity is difficult. We would therefore like to work with a complete, continuous invariant instead of working with the periodic point set itself. We conjecture that the sequence of order k persistence diagrams (will be defined in Georg Osang's talk) for all positive integers k is such a complete, continuous invariant of equivalence classes of periodic point sets.  16.2017.00 Mr Phil Smith (MIF, Liverpool)
Title. Working towards a geometric classification of crystals.
Abstract. An important problem in materials science is to be able to cluster similar crystal structures together, which will help speed up the process of materials discovery. This requires a classification of crystals quantifying how similar two structures are. We are approaching this problem from a geometric angle, looking to classify crystals based on their geometry. To this end, we introduce packing functions which computes the proportion of a unit cell of a crystal that is covered by n balls centred at the atoms of the crystal. These functions reveal critical distances dependent on the crystal's geometry, and we hope we can use this information to form a metric on crystal space that can be used to cluster datasets of crystal structures.
 9.3010.30 Prof Herbert Edelsbrunner (IST Austria)
 The 12th meeting was on Monday 4th February 2019 in Queen Mary University of London: schedule in pdf.
 10.0010.45 Primoz Skraba (QMUL) Computing Persistence in Parallel
 10.4511.30 Jon Woolf (Liverpool) Stratified Homotopy Theory
 11.4512.30 Tomaso Aste (UCL) Learning Clique Forests for Probabilistic Modeling
 14.00  14.45 Tahl Nowik (Bar Ilan University) Random knots
 14.55  15.40 Ian Leary (Southampton) Examples for Brown’s question(s) on dimensions of groups
 The 11th meeting was organised by Dr Vitaliy Kurlin as a satellite workshop at MFCS on Friday 31st August 2018 in the Materials Innovation Factory (3rd floor meeting room, building 807, square 5F on the campus map), Liverpool, UK.
 14.0014.45 Dr Hubert Wagner (IST Austria)
Title. Computing persistent homology of images with Cubicle.
Abstract. Persistent homology is gaining popularity for analyzing data coming from medical imaging, astrophysics and material science. I will focus on novel techniques for computing persistent homology of multidimensional images. In particular, I will address the eternal question: "To use, or not to use (discrete Morse theory)". A new software package, Cubicle, will be showcased and compared with existing packages.  15.1516.00 Ms Katharina Oelsboeck (IST Austria)
Title. Shape Reconstruction with Holes.
Abstract. We want to reconstruct the shape of a point clould, with focus on the holes of the resulting model. In many cases, the alpha complex of appropriate scale gives a good reconstruction. However, in some applications the holes of the model are important and there is no scale of the alpha complex that gives a satisfactory result.We define operations to change the birth and death of holes in a filtered simplicial complex, i.e., they open or close holes in a subcomplex of a fixed scale. A tripartition of the simplices, and canonical (co)chains and (co)cycles that are associated to the simplices will help us identify for which simplices we need to adapt their filtration values. These can be computed with a specific matrix reduction algorithm for persistent homology. The persistence diagram of the complex can help us guide the application of the hole operations. In the second part, we will present the Wrap complex as an alternative for shape reconstruction and will apply the hole operations on it.  16.3017.15 Mr Philip Smith (MIF, Liverpool)
Title. Skeletonization algorithms with theoretical guarantees for unorganized point clouds.
Abstract. We study the problem of approximating an unorganized cloud of points (in any Euclidean or metric space) by a 1dimensional graph or a skeleton. The following recent algorithms provide theoretical guarantees for an output skeleton: the 1dimensional Mapper, alphaReeb graphs and a Homologically Persistent Skeleton. All the three algorithms will be introduced on simple examples and then experimentally compared on the same synthetic and real data. The synthetic data are random point samples around planar graphs and sets of edge pixels obtained by a Canny edge detector on images from the Berkeley Segmentation Database BSD500. The criteria for comparison are the running time, topological types, geometric errors of reconstructed graphs.
 14.0014.45 Dr Hubert Wagner (IST Austria)

 The 10th meeting was on 30th April 2018 at the University of Southampton.
 10:3011:20 Rachel Jeitziner (EPFL) TwoTier Mapper: a userindependent clustering method for global gene expression analysis based on topology
 11:3012:00 Mariam Pirashvili (Southampton) Improved understanding of aqueous solubility modeling through Topological Data Analysis
 14:0014:50 Ginestra Bianconi (QMUL) Emergent Hyperbolic Network Geometry and Frustrated Synchronization
 15:0015:50 Grzegorz Muszynski (Liverpool) Topological Analysis and Machine Learning for Detecting Atmospheric River Patterns in a Climate Model Output

 The 9th meeting was on 2nd February 2018 in the Queen Mary University of London.
 9.3010.30 (Scape 1.04) Prof Gabor Elek (University of Lancaster) Topological graph limits
 11.0012.00 (Scape 1.04) Dr Tim Evans (Imperial College London) Networks and Spacetime
 14.0015.00 (Scape 2.01) Prof Ran Levi (Aberdeen) NeuroTopology: An interaction between topology and neuroscience
 15.3016.30 (Scape 2.01) Dr Stephan Mescher (University of Leipzig) Topological complexity of aspherical spaces
 The network was initiated by Prof Michael Farber (Queen Mary) with coorganisers at Aberdeen, Durham, Southampton.
 The first 8 meetings were in 20152016 at Aberdeen, Durham, Queen Mary, Southampton.
 The previous webpage was excellently maintained by Dr Mark Grant (Aberdeen).
Research topics of the Applied Algebraic Topology network
We run 3 halfday meetings per year with 34 talks on many topics of applied topology including (but not restricted to)
 Topology of configuration spaces of particles and mechanisms of different types (including linkages) and their applications in robotics, molecular biology and materials chemistry.
 Topology of robot motion planning, complexity of algorithms for autonomous robot motion.
 Stochastic topology (random complexes, random manifolds, random groups etc).
 Applications of Topological Data Analysis to Computer Vision, Materials Science, Climate system, pattern recognition and reconstruction of persistent topological structures in big and noisy data.
 Combinatorial and toric homotopy theory (simplicial complexes and polytopes, momentangle complexes, polyhedral products, etc).