GRK 2229:  Asymptotic Invariants and Limits of Groups and Spaces

• Subject Area: Mathematics
• Term: since 2016
• Website: Homepage
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 281869850

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 a 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 proof of Thurston’s virtual Haken conjecture, are based on the ideas of asymptotic geometry. The RTG initiative of Heidelberg University and the Karlsruhe Institute of Technology established the nationally and internationally the first systematic PhD education in this area of geometry. Our doctoral researchers investigate asymptotic invariants, deformations and moduli spaces, and convergence and limits of geometric spaces. A lively interplay and breadth of geometric techniques mark our research programme. Through strategic hirings, and new scientific developments during the first funding period, we integrated new directions, in particular the interplay between geometry and (symplectic) dynamics. We are now well positioned for the second funding period with an expanded and, with regard to the distribution onto both sites, more balanced group of PIs, which give new impulses to the RTG. Through the qualification program the PhD students acquire a methodically broad education within geometry. They get to know dynamical, analytical, group-theoretical, topological and differential-geometric aspects. Further, they acquire communication and networking skills that are key abilities of future leaders in science, academia and industry. Special mentoring activities aim at a better gender balance in mathematics. All members of the RTG benefit from the cooperation between both sites, with their complementary strengths, as well as from our connections to mathematical centers in France, Israel and the US.

• DFG Programme: Research Training Groups
• Applicant Institution: Karlsruher Institut für Technologie
• Co-Applicant Institution: Ruprecht-Karls-Universität Heidelberg
• Spokesperson: Professor Dr. Roman Sauer
• Participating Researchers: Professor Dr. Peter Albers, since 5/2018; Dr. Gabriele Benedetti; Professor Dr. Tobias Hartnick; Dr. Claudio Llosa Isenrich; Professor Dr. Manuel Krannich, since 2/2023; Professor Dr. Tobias Lamm; Professor Dr. Alexander Lytchak, since 2/2023; Professorin Dr. Maria Beatrice Pozzetti; Dr. Anja Randecker; Professorin Dr. Petra Nora Schwer, since 10/2024; Professor Dr. Wilderich Tuschmann; Professorin Dr. Anna Wienhard