Expander graphs are sparse but nevertheless sufficiently connected graphs, making them useful for constructing computer networks that are reliable as well as cost-effective. A huge area of research has emerged from this, involving both mathematics and computer science.
In recent years, a theory of simplicial complexes of dimension greater than one, sharing strong similarities with expander graphs, has begun to emerge. The known sources of examples remain however rather limited, and are all tightly related to algebraic or classical groups.
The goal of this project is to develop a new framework providing new abundant sources of examples of such high dimensional expanders. That framework is based on a non-classical family of groups, called Kac–Moody– Steinberg (KMS) groups. By unveiling the combinatorial, geometric, Lie-algebraic and cohomological properties of KMS groups and their associated geometric spaces, we will also contribute to various problems in geometric group theory concerning the residual properties of hyperbolic groups, lattice envelopes, higher degree cohomology vanishing and group stability.