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Hilbert Modular Forms and Diophantine Applications

Objective

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.
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Coordinator

THE UNIVERSITY OF WARWICK

Address

Kirby Corner Road - University House
Cv4 8uw Coventry

United Kingdom

Activity type

Higher or Secondary Education Establishments

EU Contribution

€ 161 792,99

Administrative Contact

Peter Hedges (Dr.)

Project information

Grant agreement ID: 220064

Status

Closed project

  • Start date

    20 July 2009

  • End date

    19 July 2011

Funded under:

FP7-PEOPLE

  • Overall budget:

    € 161 792,99

  • EU contribution

    € 161 792,99

Coordinated by:

THE UNIVERSITY OF WARWICK

United Kingdom