{"links":{"self":"http://dataportal.arc.gov.au/NCGP/API/grants/FT250100880"},"data":{"type":"grant-details","id":"FT250100880","attributes":{"code":"FT250100880","administering-organisation":"University of Wollongong","announcement-administering-organisation":"University of Wollongong","scheme-name":"ARC Future Fellowships","grant-status":"Active","funding-commencement-year":2025,"years-funded":4,"project-start-date":"2026-02-02","anticipated-end-date":"2030-02-01","grant-summary":"New directions in geometric flows. A geometric flow describes how an object's shape evolves under applied forces, such as a bubble floating through air or a rubber band returning to its natural shape by releasing bending energy. In this process, factors like area, volume, and curvature are optimised within given constraints. This project will explore two groundbreaking geometric flows: Sobolev curvature flow and the target flow, both specifically designed to build on the candidate's recent breakthroughs. Now is the perfect moment to drive forward transformative progress on two renowned open mathematical problems: the Cartan-Hadamard conjecture and a challenge posed by Fields Medallist S. T. Yau. Key benefits include new knowledge and research capacity building.","funding-current":1070491.00,"funding-at-announcement":1047398,"investigators-current":[{"title":"Dr","firstName":"Glen","familyName":"Wheeler","roleName":"Future Fellowship","roleCode":"FT","isFellowship":true,"orcidIdentifier":"0000-0003-3314-5647 "}],"investigators-at-announcement":[{"title":"Dr","firstName":"Glen","familyName":"Wheeler","roleName":"Future Fellowship","roleCode":"FT","isFellowship":true,"orcidIdentifier":"0000-0003-3314-5647 "}],"organisations-current":[{"organisationName":"University of Wollongong","roleName":"Administering Organisation","state":"NSW"}],"organisations-at-announcement":[{"organisationName":"University of Wollongong","roleName":"Administering Organisation","state":"NSW"}],"field-of-research":[{"isPrimary":true,"code":"4904","name":"Pure Mathematics","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":["Japan","Poland"],"lief-register":[],"achievement-summary":null,"national-interest-test-statement":"This project focuses on advancing geometric flows, mathematical constructs developed mid-20th century to model phenomena in materials science, including phase separation in alloys, grain boundary motion, and thermal grooving. Geometric flows have since found extensive applications in mathematics and physics, with new uses continually emerging. Modelling bushfire fronts—a significant issue in Australia—is a recent application. Perelman's use of Ricci flow to solve the Poincaré Conjecture, a universally acclaimed breakthrough, illustrates their impact.\nThis project aims to tackle significant mathematical problems by inventing and developing two novel geometric flows. Progress here will enhance Australia's international standing through noteworthy research. The project will establish new theoretical frameworks that can be applied to deepen understanding of other geometric flows, offering long-term benefits.\nThe project also trains the next generation of mathematicians, who will positively influence Australia's economy. It will elevate Australian mathematics and universities, attract international students, and deliver economic and cultural benefits. To promote research outcomes from the project beyond academia, I will use my established YouTube channel and Zulip server, inspiring a broad audience with cutting-edge mathematics. This initiative maximises understanding and adoption of the research, enhancing its impact."}}}