Groups and buildings

• Applicant: Professor Dr. Stefan Witzel
• Subject Area: Mathematics
• Term: from 2014 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 248383224

The goal of the project is to use the geometry of buildings to improve the understanding of certain groups that act on them.One subproject is motivated by fundamental results in algebraic K-theory. The goal is to express the homology of groups such as SL_n(k[t,t^(-1)]) in terms of the homology of SL_n(k). To this end, we want to study the action of the former group on its associated twin building and its opposition complex.The other subproject has the goal to better understand certain uniform lattices on buildings. In particular, we want to determine which of them are lattices in linear groups over local fields. Moreover, we intend to classify them up to commensurability.

• DFG Programme: Research Grants