{"links":{"self":"http://dataportal.arc.gov.au/NCGP/API/grants/FT250100160"},"data":{"type":"grant-details","id":"FT250100160","attributes":{"code":"FT250100160","administering-organisation":"The University of Sydney","announcement-administering-organisation":"The University of Sydney","scheme-name":"ARC Future Fellowships","grant-status":"Active","funding-commencement-year":2025,"years-funded":4,"project-start-date":"2026-01-05","anticipated-end-date":"2031-01-04","grant-summary":"Connection via reflections: A new approach to Coxeter groups. This project aims to use a new synthesis of approaches to investigate fundamental properties of reflection groups. These groups are central to mathematics and its applications. The project will combine algebra, combinatorics and geometry to study both the delicate structure of Kazhdan-Lusztig polynomials and the large-scale behaviour of boundaries at infinity, thus answering deep questions in the fields of representation theory and geometric group theory, respectively. The project's new combination of approaches and significant outcomes will forge innovative and productive connections between these two areas; the former is a classical field, well-established in Australia, while the latter is relatively new and internationally vibrant.","funding-current":1201153.00,"funding-at-announcement":1175732,"investigators-current":[{"title":"A/Prof","firstName":"Anne","familyName":"Thomas","roleName":"Future Fellowship","roleCode":"FT","isFellowship":true,"orcidIdentifier":"0000-0001-9074-4553 "}],"investigators-at-announcement":[{"title":"A/Prof","firstName":"Anne","familyName":"Thomas","roleName":"Future Fellowship","roleCode":"FT","isFellowship":true,"orcidIdentifier":"0000-0001-9074-4553 "}],"organisations-current":[{"organisationName":"The University of Sydney","roleName":"Administering Organisation","state":"NSW"}],"organisations-at-announcement":[{"organisationName":"The University of Sydney","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":"490405","name":"Group Theory and Generalisations","type":"FOR20"}],"socio-economic-objective":[{"code":"280118","name":"Expanding Knowledge In the Mathematical Sciences","type":"SEO20"}],"international-collaboration":["Germany","United States of America"],"lief-register":[],"achievement-summary":null,"national-interest-test-statement":"Mathematics is the language needed to effectively describe phenomena in the world around us, at scales ranging from subatomic structures to social networks to galaxies. It is the theoretical underpinning of all fundamental and applied sciences. This project investigates collections of symmetries which appear throughout mathematics and that are of central importance in crystallography, an interdisciplinary area with a key role in biology, chemistry and physics. The project will answer deep mathematical questions about these collections of symmetries, ranging from the microscopic to the infinite, by developing powerful new tools which combine, for the first time, the best ideas from two key areas of mathematical research. This will provide expansive training for the students and early-career researchers included on the project, and guide international research in these fields. The project includes two carefully-designed early-career workshops, as well as an international conference, all of which will feature many female speakers and mentors. This will forge productive new connections within Australian mathematics, foster connections between Australian and international researchers, mentor early-career researchers and women in mathematics, and enhance Australia's reputation as a leading centre for fundamental mathematical research. The theoretical advances resulting from this project will have future applications in crystallography, physics, cybersecurity and data science."}}}