Speaker
Description
I'm going to talk about a couple of cool facts about affine and linear Tits buildings for the real numbers. One is that you can get a Solomon-Tits theorem if you take any collection of hyperplanes and their intersections, rather than taking all subspaces. The other is that if you suspend the Tits building twice, then the apartments become cubes, and this leads to a beautiful geometric picture of the products and coproducts in linear Tits buildings.
As an application, we make new computations of scissors congruence groups for polytopes with restrictions on them, such as having vertices in a given number field, or only rectilinear boxes. And we describe the Hopf algebra structure on the coinvariants of the Steinberg module in a way that lifts more easily to spectra. This is joint work with Kupers, Lemann, Miller, and Sroka, and with Klang, Kuijper, Mehrle, and Wittich.
