This proposal is for a series of three Euroconferences to take place in 2001 in Rome, in 2002 in Luminy (near Marseille) and in 2003 in Porto. These form a continuation of a series organised by the international research group "Vector Bundles on Algebraic Curves" (VBAC), which was financed by the TMR programme for the years 1998-2000. These conferences have been highly successful, VBAC2000 in Bad Honnef, Germany attracting 59 participants including more than 30 young researchers.
The subject of vector bundles on algebraic curves stands at the crossroads of several areas of mathematics, involving ideas from algebraic geometry, topology, and conformal field theory and gauge theory. In particular there are strong connections with theoretical physics, which in recent years has inspired many of the developments in the subject. This research area has been at the centre of many exciting research developments and presents excellent opportunities for young researchers.
For this reason, and in view of the rapid development of the subject, high-level scientific conferences can play a key role in bringing together experts from different disciplines with researchers in the area. These conferences provide an environment encouraging exchange of ideas and can be expected to lead to significant developments and new collaborations.
The three events proposed are linked by the common theme embodied in the overall title "Vector Bundles on Algebraic Curves". Each has a particular emphasis, the first dealing especially with the geometry of moduli spaces, the second covering vertex algebras and the third concentrating on topological questions. These topics are not, however, independent, the relationships between them being of fundamental importance.
Thus each event will not only have a special emphasis but will seek to involve researchers from all areas of the subject. Participation by women researchers, researchers from less-favoured regions and researchers from the associated states will be encouraged.