Lattices of minimal covolume in simple Lie groups and applications

• Applicants: Dr. Amir Dzambic; Professor Dr. Ralf Köhl
• Subject Area: Mathematics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 515393142

Lattices of small covolume in semisimple Lie groups (over archimedian or non-archimedian local fields) lead to rich geometric structures such as Riemannian manifolds with many automorphisms or to discrete groups acting highly transitively on Bruhat-Tits buildings or to fake projective planes or to short presentations by generators and relations of these lattices. Motivated by such geometric applications we intend to classify the (arithmetic) lattices of minimal covolume in semisimple real Lie groups of higher rank. Our case-by-case investigation will depend on the classification of higher rank real Lie groups and is based on Prasad's covolume formula and on the maximality criteria of lattices by Rohlfs and by Ryzhkov and Chernousov.

• DFG Programme: Research Grants