The proposed network covers the domain of Arithmetic Algebraic Geometry, a discipline situated at the crossroad of Geometry and Number Theory. It builds on the accomplishments and experience (in both training and research) of three consecutive European networks in this field. Its structure is a direct continuation (and logical further development) of the existing Research Training Network 'AAG' that was financed under the Fifth Framework Programme, which will end in September 2003.
Arithmetic Algebraic Geometry has been an extremely active and successful domain of research over the past thirty years, and is one of the not so many domains of Pure Mathematics where European mathematicians determine the state of the art to a very large extent. To mention only one striking achievement in this field, let us recall the recent proof by Laurent Lafforgue of the celebrated Langlands conjecture over function fields. Lafforgue, a member of the Paris XI team of this proposal, was awarded for this a Fields medal - which in Mathematics plays the role of the Nobel Prize in other disciplines - at the 2002 International Mathematical Congress in Beijing. His research was carried out while he was a member of our previous networks.
The general case of the Langlands conjectures, which now more than ever is a very active and fertile area of research, is one of the core themes of this proposal, the other two being the local and global arithmetic properties of algebraic varieties. Highly visible results such as the proof of the Langlands conjecture are in fact but the tip of an iceberg, whose underlying body is represented by a broad collection of different theories, producing results which are often of foundational and technical nature. Arithmetic Algebraic Geometry borrows from virtually all areas of Mathematics, so that its methods and techniques are very diverse, composite and highly specialised. The complementary expertise of the fourteen teams of the proposed network allow the?
Call for proposal
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Funding SchemeRTN - Marie Curie actions-Research Training Networks
Bellaterra (Cerdanyola Del Valles)