{"links":{"self":"http://dataportal.arc.gov.au/NCGP/API/grants/FT250100951"},"data":{"type":"grant-details","id":"FT250100951","attributes":{"code":"FT250100951","administering-organisation":"The Australian National University","announcement-administering-organisation":"The Australian National University","scheme-name":"ARC Future Fellowships","grant-status":"Active","funding-commencement-year":2025,"years-funded":4,"project-start-date":"2026-01-02","anticipated-end-date":"2031-01-01","grant-summary":"Theory and computation of vineyards and vineyard modules. Vineyards and vineyard modules are mathematical objects calculated from topological measurements of continuous one-parameter families of data. This project aims to develop theory and computational tools for the use of vineyards and vineyard modules with a particular focus on time-varying point clouds and planar subsets as data input. The project expects to generate new knowledge relating to the algebraic and geometric structures within vineyards and vineyard modules, as well as develop new code for computing vineyards and distances between vineyards. Expected outcomes and benefits include enhanced data analysis tools, research training with increased capacity within the mathematical sciences, and increased international collaboration. ","funding-current":1314552.00,"funding-at-announcement":1286732,"investigators-current":[{"title":"A/Prof","firstName":"Katharine","familyName":"Turner","roleName":"Future Fellowship","roleCode":"FT","isFellowship":true,"orcidIdentifier":"0000-0002-6679-7441 "}],"investigators-at-announcement":[{"title":"A/Prof","firstName":"Katharine","familyName":"Turner","roleName":"Future Fellowship","roleCode":"FT","isFellowship":true,"orcidIdentifier":"0000-0002-6679-7441 "}],"organisations-current":[{"organisationName":"The Australian National University","roleName":"Administering Organisation","state":"ACT"}],"organisations-at-announcement":[{"organisationName":"The Australian National University","roleName":"Administering Organisation","state":"ACT"}],"field-of-research":[{"isPrimary":false,"code":"461305","name":"Data Structures and Algorithms","type":"FOR20"},{"isPrimary":false,"code":"490399","name":"Numerical and Computational Mathematics Not Elsewhere Classified","type":"FOR20"},{"isPrimary":true,"code":"4904","name":"Pure Mathematics","type":"FOR20"},{"isPrimary":false,"code":"490412","name":"Topology","type":"FOR20"}],"socio-economic-objective":[{"code":"280115","name":"Expanding Knowledge In the Information and Computing Sciences","type":"SEO20"},{"code":"280118","name":"Expanding Knowledge In the Mathematical Sciences","type":"SEO20"}],"international-collaboration":["England","France","United States of America"],"lief-register":[],"achievement-summary":null,"national-interest-test-statement":"Topological Data Analysis is an exciting new area of research in data science providing insights into the shape of data. Within Topological Data Analysis the mathematical object of vineyards capture information about how this shape of changes over time-varying data. Vineyards have been effective in diverse applications with dynamic data from analysis fMRI scans to music classification, but their power is hampered by the lack of algorithms to compute their algebraic and geometrical structures, and the lack of statistical tools that can utilise the information contained in these structures. This project addresses this important gap through theory development as well as mathematically informed algorithm design and implementation. The project will create accessible tools for data scientists to use for dynamic point clouds and for the analysis of shapes.\n"}}}