{"links":{"self":"http://dataportal.arc.gov.au/NCGP/API/grants/DE260100829"},"data":{"type":"grant-details","id":"DE260100829","attributes":{"code":"DE260100829","administering-organisation":"The University of New South Wales","announcement-administering-organisation":"Monash University","scheme-name":"Discovery Early Career Researcher Award","grant-status":"Active","funding-commencement-year":2026,"years-funded":3,"project-start-date":"2026-02-09","anticipated-end-date":"2029-02-08","grant-summary":"Monge–Ampère equations and optimal transport: geometry and regularity. Monge–Ampère equations and optimal transport are important fields which have played defining roles in 21st century mathematics. These topics have applications to diverse areas like fluid flow, meteorology, neural networks, and economics and also have applications in pure mathematics, for example to geometry and functional inequalities. This project will develop regularity theory for the Monge–Ampère partial differential equations (PDE) as well as investigate both the geometry and economic applications of optimal transport. This project aims to generate new mathematical theories relevant to these applications and will have significant impact and benefit on elliptic PDE, optimal transport, and Australia's global reputation in mathematics.  ","funding-current":427177.00,"funding-at-announcement":423777,"investigators-current":[{"title":"Dr","firstName":"Cale","familyName":"Rankin","roleName":"Discovery Early Career Researcher Award","roleCode":"DECRA","isFellowship":true,"orcidIdentifier":"0000-0002-6723-0308 "}],"investigators-at-announcement":[{"title":"Dr","firstName":"Cale","familyName":"Rankin","roleName":"Discovery Early Career Researcher Award","roleCode":"DECRA","isFellowship":true,"orcidIdentifier":"0000-0002-6723-0308 "}],"organisations-current":[{"organisationName":"The University of New South Wales","roleName":"Administering Organisation","state":"NSW"}],"organisations-at-announcement":[{"organisationName":"Monash University","roleName":"Administering Organisation","state":"VIC"}],"field-of-research":[{"isPrimary":false,"code":"380303","name":"Mathematical Economics","type":"FOR20"},{"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":["Canada","China (excludes SARs and Taiwan)"],"lief-register":[],"achievement-summary":null,"national-interest-test-statement":"This project develops new tools in the mathematical fields of optimal transport and elliptic partial differential equations (PDE). These are important and active areas of modern mathematics for which improving our understanding will help us better understand problems in meteorology, economics, and machine learning. By advancing these mathematical foundations, this project could lead to more efficient models and solutions for challenges in areas like resource allocation, weather forecasting, and economic modeling. In addition, pure mathematics research benefits Australia by enhancing our national mathematical expertise and international standing. Australia will experience cultural and economic benefits through this enhanced global reputation, attracting top international researchers and fostering new collaborations, all of which improve the educational opportunities available to Australians in the area of mathematics.  The results obtained in this DECRA will be shared open access to ensure this research is available to everyone including those outside academia such as industry partners, peak bodies or other consumer/stakeholder groups. Monash has strong networks with industry partners which may assist with research translation by making the highly applicable components of this project available to users. "}}}