{"links":{"self":"http://dataportal.arc.gov.au/NCGP/API/grants/FT250100834"},"data":{"type":"grant-details","id":"FT250100834","attributes":{"code":"FT250100834","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":"2026-06-30","anticipated-end-date":"2030-06-30","grant-summary":"The atomic structure of ancient flows. The proposed research aims to develop a novel approach to the analysis of ancient solutions to a very general class of (both extrinsic and intrinsic) geometric flows. The new ideas will lead to a complete classification of positively curved ancient solutions in low dimensions, which will have far-reaching consequences for the understanding of singularities in such equations, opening the door to many new and significant applications.","funding-current":1117666.00,"funding-at-announcement":1093436,"investigators-current":[{"title":"Dr","firstName":"Mat","familyName":"Langford","roleName":"Future Fellowship","roleCode":"FT","isFellowship":true,"orcidIdentifier":null}],"investigators-at-announcement":[{"title":"Dr","firstName":"Mat","familyName":"Langford","roleName":"Future Fellowship","roleCode":"FT","isFellowship":true,"orcidIdentifier":null}],"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":true,"code":"4904","name":"Pure Mathematics","type":"FOR20"},{"isPrimary":false,"code":"490402","name":"Algebraic and Differential Geometry","type":"FOR20"},{"isPrimary":false,"code":"490410","name":"Partial Differential Equations","type":"FOR20"}],"socio-economic-objective":[{"code":"280118","name":"Expanding Knowledge In the Mathematical Sciences","type":"SEO20"}],"international-collaboration":["England","United States of America"],"lief-register":[],"achievement-summary":null,"national-interest-test-statement":"In many physical systems, a geometric structure (such as an interface or a Riemannian metric) changes over time in a manner dependent on its curvature. Examples include erosion processes like stones tumbling on the beach and the propagation of bushfire fronts. Often, these evolutionary processes are highly nonlinear, and form \"singularities\", the onset of which is an obstruction to a classical analysis. A robust method to understand (and overcome) singularity formation involves the characterisation of \"ancient solutions\". This project addresses the research gap in the analytical understanding of ancient solutions to a general class of (both extrinsic and intrinsic) curvature driven geometric flows. The mathematical understanding of these processes developed in this project could lead to improvements in applications such as bushfire modelling, of critical significance in Australia. Research outcomes could be promoted beyond academia to organisations that rely on these or related models, so they can make adjustments to their operations with potential economic, environmental and health benefits. Graduates and early career researchers from the research training element of this program could be directly placed into jobs with such organisations to realise this research translation. The ANU has a well-established team ready to assist with research translation by connecting these researchers with users in bushfire modelling and in other practical applications."}}}