Activities of the Network in 2000:

• Midterm Review Meeting and Postdoc Conference, Bielefeld, Febr. 29 -- March 4, 2000, organized by Ina Kersten and Ulf Rehmann.
• International Conference in CIRM (Marseille-Luminy): Up to Homotopy, 19-23 June 2000. Organized by Jean-Louis Loday and Daniel Guin.
• CONFERENCE ON ALGEBRAIC K-THEORY AND HOMOTOPY THEORY OF SCHEMES (Preliminary announcement)
  Site : Université Paul Sabatier, Departement de Mathematiques 118, route de Narbonne, 31062 Toulouse-Cedex, FRANCE
  Dates: Monday 3, July 2000 - Friday 7, July 2000
  This is the week before the 3rd European Congress of Mathematics in Barcelona, 10 July - 14 July (http://www.iec.es/3ecm/).
  PROGRAM. Among those who have already agreed to speak are : Spencer Bloch, Eric Friedlander, Marc Levine, Markus Rost, Carlos Simpson, Masaki Hanamura, Annette Huber, Emmanuel Peyre, Burt Totaro
  Scientific Committee : Bruno Kahn, Max Karoubi, Georges Maltsiniotis, Fabien Morel, Christophe Soule, Joseph Tapia
  

Further coordinated workshops on actual topics, among them:
• Thanksgiving Workshop on Controlled Topology, Geometry and Algebra, organized by H. J. Munkholm.
• Workshop on various topics of the project, organized by C. Pedrini.

1999:

• Conférence "Algèbre homotopique", Strasbourg, March 25 - 28, 1999, organized by Jean-Louis Loday (Strasbourg) and Teimuraz Pirashvili (Tbilisi).
• Workshop on Algebraic Cycles, Genova, March 26 - 28, 1999, organized by Alberto Albano, Luca Barbieri Viale, Gian Pietro Pirola..
• Oberwolfach Conference on Quadratic and Hermitean Forms, May 16 - 22, 1999, organized by Albrecht Pfister (Mainz), Winfried Scharlau (Münster), Jean-Pierre Tignol (Louvain-la-Neuve).
• Workshop on Quadratic Forms and Related Topics, Besancon, May 25 -28, 1999, organized by Eva Bayer-Fluckiger and Detlev Hoffmann.
• Mini-Summer-School "Involutions et groupes algebriques". Le 7,8 et 9 juin a la faculte Jean Perrin, rue Jean Souvraz a Lens. Organisateurs : J. Buresi, P. Mammone, J-P. Tignol.
• Conference on "Quadratic Forms and their Applications" in Dublin, July 4-10, 1999, organized by E. Bayer (Besancon), D. Lewis (Dublin) and A. Ranicki (Edinburgh).
• Oberwolfach Conference on Algebraic K-Theory, Sept. 26 - Oct. 2, 1999, organized by Daniel R. Grayson (Urbana), Uwe Jannsen (Köln), Bruno Kahn (Paris)

• SUMMER SCHOOL on "K-Theory and Algebraic Groups", June 28-July 3 1998, in Trento, organized by C. Pedrini
• Conference on Linear Algebraic Groups and Related Structures, Aug. 9-15, 1998 in Bielefeld, organized by I. Kersten, A. Merkurev, U. Rehmann.
• Conference on Topology and Geometry, Aug. 9-15, 1998 in Aarhus, organized by Karsten Grove, Ib Madsen and Erik Kjær Pedersen.
  The two above conferences are satellite conferences of the International Congress of Mathematicians, Berlin, 1998

• Network Coordinator:
  Ulf Rehmann, Fakultät für Mathematik, Universitätsstraße 25,
  Universität Bielefeld,
  D-33501 Bielefeld, Germany
  Tel +49 521 106 5039, Fax +49 521 106 4743
  e-mail: rehmann@mathematik.uni-bielefeld.de

• Local Coordinators at EC Countries:

• Claus Scheiderer, Universität Duisburg, Germany
• Manfred Knebusch, Universität Regensburg, Germany
• Eva Bayer-Fluckiger, Université de Franche Comté, Besancon, France
• Max Karoubi, Université Paris 7-Denis Diderot, France
• Jean-Louis Loday, Université Louis Pasteur, Strasbourg, France
• Jean-Pierre Tignol, Université catholique de Louvain, Belgium
• Claudio Pedrini, Universitá di Genova, Italy
• David Lewis, University College Dublin, Ireland
• Hans-J. Munkholm, Odense Universitet, Denmark
• Local Coordinators at Non-EC Countries:

• Viacheslav Yanchevskii, Institute of Mathematics, National Academy of Sciences, Belarus
• Teimuraz Pirashvili, A. Razmadze Mathematical Institute, Georgia
• Andrei Suslin, St. Petersburg Branch of Steklov Mathematical Institute, Russian Academy of Sciences, Russia

Postdoc Positions to be offered by the Project

Postdoc vacancies of the network

Research Objectives

All these disciplines are closely related in various aspects and they are vivid fields in the sense that they produce an abundance of stimulating and fascinating problems.

It is the objective of this network project to perform advanced research in the fields of Algebraic K-Theory, Linear Algebraic Groups and Related Structures, by using methodological approaches from algebra and topology.

``Related Structures'' are for example manifolds, schemes, quadratic or Hermitian forms, Azumaya algebras, Lie algebras, Brauer groups, and their associated homology and cohomology theories.

It is the main objective of this proposal to bring together the expertises of these distinct fields in order to promote their research significantly by mutual benefit, and, in particular, to attract young researchers at the postdoc level into this broad area by international exchange and intensive training.

Main research areas will be: Stable K-theory and Hochschild homology, K-theory of spaces, equivariant K-theory, algebraic models of spaces, Leibniz homology, controlled K-theory, K-theory of varieties, linear algebraic groups over arbitrary fields, projective homogeneous varieties, Hasse principles for principal homogeneous spaces and other objects, splitting varieties, quadratic forms over arbitrary fields, trace forms, Azumaya algebras, algebras with involution, Chow groups, Brauer groups, R-equivalence and birational questions, toric varieties, cohomology ring of finite group schemes.

The detailed Work Programme: Postscript

Some historical remarks and illustrations concerning certain aspects of the research by this network can be found here.

Results and Achievements (Dec, 1, 1997 -- Nov. 30, 1998):

During the reporting period, several manuscripts and one monograph (``The book of involutions'', 580 pages) have been published involving two or three network partners each; several others of this type have been produced as preprints or have been announced. These manuscripts describe results on algebras with and without involutions, quadratic froms, various algebraic groups, in particular on unitary and on orthogonal as well as on exceptional groups, and also on cylic homology. In particular, the publication of the monograph is a milestone of the project:

This book is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. It provides the algebra-theoretic foundations for much of the recent work on linear algebraic groups over arbitrary fields.

The research of the network was certainly stronly enhanced and influenced by the following three major networking activities:

• Summer School on ``K-Theory and algebraic groups'', June 28 -- July 3, 1998 (Levico Terme Italy, organized by C.~Pedrini with a scientific committee from two other participants. This had a particular training effect, since high level curses for researchers on the postdoc level have been given. There have been two sessions: a morning session where the following 4 series of lecture have been given: 1) An introduction to K-Theory and its recent developments. 2) K-Theory and Algebraic Groups. 3) K-Theory of algebraic integers. 4) K-theory and quadratic forms over fields. Written notes oof these curses were distributed to all participants. In the afternoon sessions there have been 11 research talks given by young researchers on topics concerning K-theory, algebraic groups, number theory, algebraic geometry, quadratic forms, Brauer groups etc. g
• Conference on ``Linear Algebraic Groups and Related Structures'', August 9 -- 15, 1998 (University of Bielefeld, Germany), organized by I. Kersten and U. Rehmann. 32 Talks were given (45-60 min each), 67 participants from 17 countries attended the conference. This conference was funded by SFB 343 ``Diskrete Strukturen in der Mathematik'' at the University of Bielefeld, by this TMR project, and by INTAS project INTAS-93-2618-EXT.
• Conference on ``Geometry and Topology'', August 9 -- 15, 1998 (University of Aarhus, Denmark), organized by K. Grove, I. Madsen, E. K. Pedersen. 51 Talks were given (45-60 min each), 139 participants attended the conference.

Last Updated: 21-01-2000