June 6th, 2023

Jeffrey Danciger (UT Austin)

Title

Affine geometry and the Auslander Conjecture

Abstract 

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.

Schedule

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

HD