AG-Soyuz (Europe--NIS algebraic geometry network)
INTAS reference number 93-2805 and 93-2805 Ext
period: 1st Dec 1995 - 1st Jan 1998 and 1st Sep 1998 - 31st Mar 2000

Coordinator:
Miles Reid (Room 140)          tel: +44 (0) 24 (Coventry) 76523491 (office)
Math Inst., Univ. of Warwick     home tel: +44 (0) 1926 (Kenilworth) 857929
Coventry CV4 7AL, England               Math Inst. Fax: +44 (0) 24 76524182
e-mail: Miles@Maths.Warwick.Ac.UK       web: www.maths.warwick.ac.uk/~miles

Summary
The Western partners in the project are Warwick, the Abdus Salam ICTP
(Trieste) and Univ. Kaiserslautern, Fachbereich Mathematik.

The NIS partner is Steklov Inst., Moscow, but AG-Soyuz also involves
collaboration with a network including Moscow (several institutions),
Vladimir, Yaroslavl', Samara, Kharkov, Kiev and St Petersburg.

An important aspect of our work has involved providing practical
assistance to NIS mathematicians within the NIS (computing equipment and
library supplies). The other aim is research collaboration in algebraic
geometry and related subjects, including visits of NIS mathematicians to
European centres.

Mathematicians involved in our project have visited many world math
research centres, lectured at international conferences and produced well
over a hundred papers and preprints. Many of these are available as
preprints on the alg-geom eprint file server formerly at Duke, now at
http://xxx.lanl.gov/ with European mirror sites at xxx.soton.ac.uk (UK),
xxx.lpthe.jussieu.fr (France), and xxx.uni-augsburg.de (Germany).

Some of our highlighted research projects are as follows:
 (a) Higher dimensional birational geometry (Corti, Iskovskikh, Prokhorov,
Pukhlikov, Reid)
 (b) Derived categories of coherent sheaves and Fourier--Mukai transform
(Bondal, Bridgeland, King, Markarian, Orlov, Thomas, Reid)
 (c) Special Lagrangian geometry, the Strominger--Yau--Zaslow approach to
mirror symmetry, geo\-metric quantisation and Bohr--Sommerfeld orbits
(Gross, Hitchin, Tyurin)
 (d) Classifying the modules over singular curves in representation
theoretic type, enumerating the simples case (Drozd and Greuel)
 (e) Higher dimensional local fields, adelic group and applications
(Abrashkin, Fesenko, Parshin, Vostokov)