Cel Elliptic curves are the heart of contemporary research in number theory. For example, their modularity played a crucial role in Wiles' proof of Fermat's Last Theorem. Understanding their rational points is the subject of the Birch and Swinnerton-Dyer Conjecture (BSD), one of the seven $1M Clay Mathematics Institute Millennium Prizes. This proposal is concerned with rational points on elliptic curves and linked to both BSD and modularity.The Darmon Programme is an ambitious project initiated by Henri Darmon, aiming to provide constructions of points on elliptic curves over number fields, and to prove new cases of BSD. The proposed action is an initiative to extend the Darmon Programme, make known constructions explicit and algorithmic to provide extensive data that will be invaluable to researchers in the field, and guide further theoretical work.Warwick has one of the largest and most active explicit number theory groups in the world, consisting of 2 professors, 3 lecturers, 8 research fellows and 12 PhD students, making it a natural host for the project. The supervisor Siksek, is a leading expert on elliptic curves, rational points and modularity, with considerable experience in supervising research including 5 Marie Curie fellows.Masdeu did his undergraduate studies in Barcelona. He completed his PhD (McGill) under the supervision of Darmon, and therefore has intimate understanding of the Darmon Programme. Masdeu then worked as Ritt Assistant Professor at Columbia University before joining Warwick as a postdoc in 2014. Therefore his research experience has almost entirely been confined to North America, even though his ambition is to establish himself as an independent researcher at a prestigious European university. Masdeu has substantial research results with 8 papers accepted in strong journals. This project will integrate him into the European research environment, and give him new skills and research directions to enable him to realize his goal. Dziedzina nauki natural sciencescomputer and information sciencessoftwarenatural sciencescomputer and information sciencescomputer securitycryptographynatural sciencesmathematicspure mathematicsarithmetics Słowa kluczowe Modular symbols Modularity Shimura Curves Stark-Heegner points Darmon points Program(-y) H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility Temat(-y) MSCA-IF-2014-EF - Marie Skłodowska-Curie Individual Fellowships (IF-EF) Zaproszenie do składania wniosków H2020-MSCA-IF-2014 Zobacz inne projekty w ramach tego zaproszenia System finansowania MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF) Koordynator THE UNIVERSITY OF WARWICK Wkład UE netto € 195 454,80 Adres Kirby Corner Road - University House CV4 8UW Coventry Zjednoczone Królestwo Zobacz na mapie Region West Midlands (England) West Midlands Coventry Rodzaj działalności Higher or Secondary Education Establishments Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Uczestnictwo w unijnych programach w zakresie badań i innowacji Opens in new window sieć współpracy HORIZON Opens in new window Koszt całkowity € 195 454,80