Welcome to RTG 2229
"Asymptotic Invariants and Limits of Groups and Spaces"
Asymptotic geometry investigates macroscopic properties of geometric spaces. It looks at geometric spaces from afar. The difference between a continuous geometric space and its discrete approximations thus vanishes. This leads to unified framework to study discrete as well as continuous geometric structures. Many breakthroughs in geometry, ranging from Mostow's and Margulis' rigidity theorems to Agol's recent proof of Thurston's virtual Haken conjecture, are based on the ideas of asymptotic geometry.
Despite its importance in modern geometry, a framework of doctoral education and research that takes the perspective of asymptotic geometry as its leitmotif has been missing so far. Our Research Training Group, consisting of scientists from Heidelberg and Karlsruhe, builds on the perspective of asymptotic geometry and intends to create a model for a cross-boundary geometric education of PhD students.