{"links":{"self":"http://dataportal.arc.gov.au/NCGP/API/grants/DE260101508"},"data":{"type":"grant-details","id":"DE260101508","attributes":{"code":"DE260101508","administering-organisation":"The University of New South Wales","announcement-administering-organisation":"The University of New South Wales","scheme-name":"Discovery Early Career Researcher Award","grant-status":"Active","funding-commencement-year":2026,"years-funded":3,"project-start-date":"2026-01-01","anticipated-end-date":"2028-12-31","grant-summary":"Higher-order Fourier analysis: discerning structure from randomness. Despite having only arisen in the past 25 years, higher-order Fourier analysis has yielded remarkable breakthroughs in mathematics, including in combinatorics (e.g., around Szemerédi’s theorem), number theory (e.g., the Green-Tao theorem), ergodic theory, and theoretical computer science. Given the youth of the subject, understanding of it is in its infancy. This project aims to develop frameworks for understanding the generalised oscillatory patterns underlying higher-order Fourier analysis. These frameworks will be used to resolve major open problems about pseudorandomness in the above contexts, place Australia at the forefront of knowledge in this nascent area, and foster international collaboration in the many areas to which it applies.","funding-current":419408.00,"funding-at-announcement":416079,"investigators-current":[{"title":"Dr","firstName":"Daniel","familyName":"Altman","roleName":"Discovery Early Career Researcher Award","roleCode":"DECRA","isFellowship":true,"orcidIdentifier":null}],"investigators-at-announcement":[{"title":"Dr","firstName":"Daniel","familyName":"Altman","roleName":"Discovery Early Career Researcher Award","roleCode":"DECRA","isFellowship":true,"orcidIdentifier":null}],"organisations-current":[{"organisationName":"The University of New South Wales","roleName":"Administering Organisation","state":"NSW"}],"organisations-at-announcement":[{"organisationName":"The University of New South Wales","roleName":"Administering Organisation","state":"NSW"}],"field-of-research":[{"isPrimary":true,"code":"4904","name":"Pure Mathematics","type":"FOR20"},{"isPrimary":false,"code":"490401","name":"Algebra and Number Theory","type":"FOR20"},{"isPrimary":false,"code":"490404","name":"Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)","type":"FOR20"},{"isPrimary":false,"code":"490406","name":"Lie Groups, Harmonic and Fourier Analysis","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":"For 200 years, Fourier analysis has been a fundamental tool in mathematics, science and engineering, allowing functions to be decomposed into waves in order to distinguish structured signals from random noise. However, classical Fourier analysis can only detect linear structure and discards more intricate nonlinear structure as \"noise.\" Higher-order Fourier analysis is designed to capture these nonlinear structures, and although a much younger field, has yielded remarkable breakthroughs in a diverse set of problems. This project aims to develop new methodologies that extend the reach of higher-order Fourier analysis, providing more powerful tools for detecting arithmetic structure in complex data and advancing the theoretical foundations that underpin its applications.\n\nThis project will provide mathematical insights relevant to cryptography, machine learning, and artificial intelligence, which all rely on extracting information from data, and distinguishing structure from randomness. Strengthening Australia’s research in this area will also promote international collaboration, not only making Australia attractive to international experts in this area, but also to researchers in the myriad and diverse areas to which these techniques apply. \n"}}}