COMPAUTGALREP

Computations of Automorphic Galois Representations

Coordinatore	THE UNIVERSITY OF WARWICK    more  Organization address address: Kirby Corner Road - University House - city: COVENTRY postcode: CV4 8UW contact info Titolo: Dr. Nome: Peter Cognome: Hedges Email: send email Telefono: +44 247 652 3716 Fax: +44 2 476524991
Nazionalità Coordinatore	United Kingdom [UK]
Totale costo	164˙540 €
EC contributo	164˙540 €
Programma	FP7-PEOPLE Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	FP7-PEOPLE-2009-IEF
Funding Scheme	MC-IEF
Anno di inizio	2010
Periodo (anno-mese-giorno)	2010-07-01   -   2012-06-30

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	THE UNIVERSITY OF WARWICK  Organization address address: Kirby Corner Road - University House - city: COVENTRY postcode: CV4 8UW contact info Titolo: Dr. Nome: Peter Cognome: Hedges Email: send email Telefono: +44 247 652 3716 Fax: +44 2 476524991	UK (COVENTRY)	coordinator	164˙540.80

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 Obiettivo del progetto (Objective)

'In groundbreaking work, the researcher has developed the first ever algorithm for explicitly determining the mod l-Galois representations of classical modular forms. He has applied this to the Inverse Galois Problem and to Lehmer's Conjecture on the non-vanishing of the Ramanujan tau-function. Arguably the greatest advance in arithmetic geometry within the last decade has been the proof by Khare and Wintenberger of Serre's Conjectures over the rationals. A version of Serre's Conjectures over totally real fields has been suggested by Buzzard, Diamond and Jarvis, complete with explicit formulae for the Serre 'weights' and 'levels'. The broad objectives of the proposal are as follows: 1. Improve the researcher's algorithms for the explicit determination of mod l-Galois representations of classical modular forms. 2. Give a corresponding algorithm for Hilbert modular forms. 3. With the help of 2, provide systematic evidence for Serre's Conjectures over real quadratic fields. 4. Systematically apply the Galois representations of classical and Hilbert modular forms to the Inverse Galois Problem.'