Prof Vitaliy Kurlin: mathematics & computer science

Annual MACSMIN : Mathematics and Computer Science for Materials Innovation

The MACSMIN logo includes the basic examples of the rock-salt cubic crystal, the benzene ring, and a blue wave containing a local maximum and a local minimum.

Contents : MACSMIN vision, highlights and past meetings

• Vision of the annual conference series MACSMIN
• The 6th MACSMIN on 8-12 September 2025
• The 5th MACSMIN on 9-13 September 2024
• The 4th MACSMIN on 22-25 May 2023
• The 3rd MACSMIN on 5-9 September 2022
• The 2nd MACSMIN on 15-17 September 2021
• The 1st MACSMIN conference on 7-8 September 2020
• The MIF++ seminar is a continuous version of MACSMIN
• The history : earlier meetings, BAMC 2021, SIAM MS 2021.

Vision of the annual conference MACSMIN

• We aim to create an inter-disciplinary community on the interface between Mathematics, Computer Science, Materials.
• A discovery of new materials can be substantially accelerated by using rigorous foundations from Mathematics and justified algorithms from Computer Science, which outperform brute-force blind sampling on powerful supercomputers.
• The ultimate goal is a geometry-based inverse design of new materials for industrial applications, for example with the Cambridge Crystallographic Data Centre and IBM Research, to tackle real-life problems such as Climate Emergency.
• We welcome original contributions with theoretical results or an analysis of algorithms that can potentially help in a discovery and design of materials with desired properties, e.g. the example topics include (and are not limited to)
  • Geometric Data Science : moduli spaces of unlabelled point clouds, molecules, and periodic structures;
  • Computational Structural Biology : spaces of proteins, folding of proteins and other biomolecules;
  • Mathematical Crystallography : moduli spaces of lattices, periodic crystals, and quasicrystals;
  • Functional Materials : algorithms for Crystal Structure Prediction (both organic and inorganic).

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Highlights : new areas and results presented at MACSMIN

• MACSMIN 2020 introduced a new area of Periodic Geometry to study moduli spaces of periodic structures (lattices and solid crystalline materials) under rigid motion or isometry, which expanded to a wider area of Geometric Data Science.
• MACSMIN 2021 presented the Crystal Isometry Principle saying that any real periodic crystal is uniquely determined by precisely enough geometry (or the isometry class) of its periodic set of only atomic centres without chemical elements.
• MACSMIN 2022 expanded traditional crystallography based on discrete symmetries to continuous crystallography, where any symmetry group is represented by a low-dimensional subspace in the full continuous space of all periodic structures.
• MACSMIN 2023 extended Geometric Data Science to the geometry of proteins by introducing complete invariants of protein backbones under rigid motion, which quickly detected thousands of duplicate chains in the Protein Data Bank.
• MACSMIN 2024 presented the Principle of Molecular Rigidity saying that the rigid conformation of any real molecule is uniquely determined by precise enough geometry (rigid equivalence class) of only atomic centres without any labels.

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History : past workshops and symposia before MACSMIN

Since 2016 we have organised several workshops in Applied Geometry and Topology :

• Topological Data Analysis for Materials Science and Engineering (4 talks), March 2016, Glasgow.
• 11th meeting (3 talks) of the UK network Applied Algebraic Topology, August 2018, Liverpool.
• 13th meeting (5 talks) of the UK network Applied Algebraic Topology, August 2019, Liverpool.
• Mini-symposium "Mathematics for Materials Science" on 9th April 2021 at the British Applied Mathematical Colloquium.
  Pawel Dlotko (Dioscuri centre, Warsaw). Computational topology tools in material science (pdf slides).
  Vitaliy Kurlin (Liverpool MIF). Introduction to Periodic Geometry for materials applications.
  Matt Bright (Liverpool MIF). Introduction to Periodic Topology for Textiles and Crystals (pdf slides).
  Frank Lutz (TU Berlin). Reconstructing metallic foams from tomography data.
  Mark Haw (Strathclyde). From clusters to chains and labyrinths.
  Teresa Heiss (IST Austria). A Topological Fingerprint for Periodic Crystals (pdf slides).
• Mini-symposium "Computational Geometry, Topology and Symmetry meet Materials Science" at SIAM MS 2021.
  • 24 May 2021 session MS25-1 abstracts at the SIAM MS EasyChair webpage (Spain times)
    13.00-13.30 Mois Ilia Aroyo. Online Materials Studies by the Bilbao Crystallographic Server (pdf slides).
    13.30-14.00 Gemma de la Flor. The study of layer and multilayer materials using the Bilbao Crystallographic Server (pdf).
    14.00-14.30 Paul Benjamin Klar. Exploiting superspace symmetry for characterizing modulation functions with first-principles calculations.
    14.30-15.00 Sergey Aksenov. Polytypic and symmetry relations between Na2Mn3(SO4)4 polymorphs.
  • 24 May 2021 session MS25-2 abstracts at the SIAM MS EasyChair webpage (Spain times)
    16.30-17.00 Jan Felix Senge. An approach towards novel roughness parameters for shot peened surfaces.
    17.00-17.30 Alexander Smith. Data Analysis in Soft Matter and Molecular Simulations (pdf slides, 7.2M).
    17.30-18.00 Lou Kondic. From topology of force networks to avalanche prediction in sheared particulate systems.
    18.00-18.30 Jeremy Mason. Comparing Local Atomic Environments by the Gromov-Wasserstein Distance (pdf slides).
  • 25 May 2021 session MS25-3 abstracts at the SIAM MS 2021 EasyChair webpage (Spain times)
    13.00-13.30 Ma Louise Antonette De Las Peñas. Symmetry Groups of Tilings on a Klein Bottle.
    13.30-14.00 Giuliana Indelicato. Symmetry in structural biology: from viral capsids to self-assembling nanoparticles.
    14.00-14.30 Yongjin Lee. Development of Nanoporous Materials Using Computational Modeling combined with Topological Data Analysis
    14.30-15.00 Sergio Ardanza-Trevijano. Persistent homology on particulate media from the observed position of the particles.
  • 26 May 2021 session MS25-4 abstracts at the SIAM MS EasyChair webpage (Spain times)
    13.00-13.30 Vitaliy Kurlin. Introduction to Periodic Geometry for applications in Materials Discovery.
    13.30-14.00 Philip Smith. A continuous, complete, isometry classification of crystals (pdf slides).
    14.00-14.30 Marco Michele Mosca. The asymptotic behaviour and a near linear time algorithm for isometry invariants of periodic sets (pdf slides).
    14.30-15.00 Daniel Widdowson. Visualisation of large crystal datasets by using TreeMaps and isometry invariants (pdf).
  • 27 May 2021 session MS25-5 abstracts at the SIAM MS EasyChair webpage (Spain times)
    14.00-14.30 Olga Anosova. An isometry classification of periodic point sets (pdf slides, 0.7M).
    14.30-15.00 Matthew Bright. Continuous metrics on the space of isometry classes of lattices.
  15.00-15.30 Teresa Heiss. A Topological Fingerprint for Periodic Crystals (pdf slides).
  15.30-16.00 Aditi Krishnapriyan. Machine learning with persistent homology and chemical word embeddings improves predictive accuracy and interpretability in metal-organic frameworks.