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Contenuto archiviato il 2024-05-28

Hilbert Modular Forms and Diophantine Applications

Obiettivo

The ideas of Frey, Serre, Ribet and Wiles connect Diophantine equations to Galois representations arising from automorphic forms. The most spectacular success in this direction is Wiles' amazing proof of Fermat's Last Theorem. The proof relates hypothetical solutions of the Fermat equation with elliptic modular forms which are the most basic (and best understood) of automorphic forms. It has become clear however, thanks to the work of Darmon and of Jarvis and Meekin, that the resolution of many other Diophantine problems lies through an explicit understanding of the more difficult Hilbert modular and automorphic forms. This project has the following aims: 1. Develop and improve algorithms for Hilbert modular forms and for automorphic forms on unitary groups. 2. To solve several cases of the generalized Fermat equation after making explicit the strategies of Darmon and of Jarvis and Meekin and computing/studying the relevant Hilbert modular forms. 3. To make precise and explicit certain instances of the Langlands programme.

Invito a presentare proposte

FP7-PEOPLE-2007-4-2-IIF
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Coordinatore

UNIVERSITY OF WARWICK
Contributo UE
€ 161 792,99
Indirizzo
KIRBY CORNER ROAD UNIVERSITY HOUSE
CV4 8UW COVENTRY
Regno Unito

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Regione
West Midlands (England) West Midlands Coventry
Tipo di attività
Higher or Secondary Education Establishments
Contatto amministrativo
Peter Hedges (Dr.)
Collegamenti
Costo totale
Nessun dato