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High-dimensional expansion, KMS groups and the opposite complex of a spherical building.

Inga Valentiner-Branth (Gent University)
Tuesday 16 June 2026 15:15 – 16:15 Aud. D1 (1531-113)
Mathematics Seminar

High-dimensional expanders (HDX) arise from generalizing the notion of expansion for graphs to (higher-dimensional) simplicial complexes. Like their one-dimensional versions, HDX have proven to be useful in theoretical computer science, but only a few constructions are known at this point. In this talk, I will introduce coboundary and cosystolic high-dimensional expansion and explain why spherical buildings and the complex opposite a fixed chamber in a spherical building are very good expanders. As for expander graphs, we are not just interested in single examples but infinite families of HDX of bounded degree. To this end, we start with an infinite complex constructed from a Kac-Moody-Steinberg (KMS) group, which is an amalgamated product of certain unipotent subgroups of Chevalley groups. The abundance of finite quotients of the KMS group gives rise to an infinite family of finite simplicial complexes that locally look like opposite complexes of spherical buildings. We will use the good expansion of the opposite complexes together with local-to-global results for high-dimensional expansion to show the desired outcome.

Organised by: Padic
Contact: Corina Ciobotaru Revised: 13.05.2026