June 6th, 2023

  • Date:

    June 6th, 2023

  • Speaker:

    Jeffrey Danciger (UT Austin)

  • Title

    Affine geometry and the Auslander Conjecture


    The Auslander Conjecture is an analogue of Bieberbach's theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichmüller theory will enter the picture.



    10:00 - 11:30 RTG Lecture 1 (Zachary Greenberg) | 5. OG, Konferenzraum

    11:30 - 12:00 Get-Together with speaker | 5. OG, Konferenzraum

    12:00 - 13:00 Common lunch | reserved at BräuStadel

    13:00 - 13:30 Informal meeting of PhD students | 5. OG, Common Room

    13:30 - 14:30 RTG colloquium: Prof. Jeffrey Danciger | EG Seminarraum B

    14:30 - 15:30 Common tea | 5. OG, Common Room

    15:30 - 17:00 RTG Lecture 2 (Julia Heller)| 5. OG, Konferenzraum

  • Place: