JournalsowrVol. 4 / No. 2DOI 10.4171/owr/2007/22

Algebraic Groups

  • Michel Brion

    Université Grenoble I, Saint-Martin-d'Hères, France
  • Jens Carsten Jantzen

    University of Aarhus, Denmark
  • Raphaël Rouquier

    Oxford University, United Kingdom
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The workshop continued a series of Oberwolfach meetings on algebraic groups, started in 1971 by Tonny Springer and Jacques Tits who both attended the present conference. This time, the organizers were Michel Brion, Jens Carsten Jantzen, and Rapha\"{e}l Rouquier. During the last years, the subject of algebraic groups (in a broad sense) has seen important developments in several directions, also related to representation theory and algebraic geometry. The workshop aimed at presenting some of these developments in order to make them accessible to a "general audience" of algebraic group-theorists, and to stimulate contacts between participants. Each of the first four days was dedicated to one area of research that has recently seen decisive progress: \begin{itemize} \item structure and classification of wonderful varieties, \item finite reductive groups and character sheaves, \item quantum cohomology of homogeneous varieties, \item representation categories and their connections to orbits and flag varieties. \end{itemize} The first three days started with survey talks that will help to make the subject accessible to the next generation. The talks on the last day introduced to several recent advances in different areas: arithmetic groups, eigenvalue problems, counting orbits over finite fields, quivers and reflection functors. In order to leave enough time for fruitful discussions, the number of talks (generally of one hour) was limited to four per day. Besides the scientific program, the participants enjoyed a piano recital on Thursday evening, by Harry Tamvakis. The workshop was attended by 53 participants, coming mainly from Europe and North America. This includes 6 PhD students, supported by the Marie Curie program of the European Union. The organizers are grateful to the EU for this support, and to the MFO for providing excellent working conditions.