spherical buildings

Bielefeld Buildings Conspiracy

The 28th edition of the Buildings conference is held in Ghent (where I am currently based) this September. [Note that this is unrelated to the actually buildings which you live and work in. The mathematical branch of building theory is abstract algebra. I have one post mentioning them.] Now I am not in the habit of announcing conferences here, so why this post? (It isn’t a good reason.) I just had a look at the list of invited speakers on the conference homepage (accessed on 24 August 2022, 22:04, Belgian time):

Only one “tba”. For the University of Bielefeld. Among all “silly” conspiracy theories, the Bielefeld conspiracy (in short: Bielefeld does not exist) might be the most popular one: Tom Scott made a video about it, Angela Merkel referenced it in a speech, people, who claim to be from Bielefeld, regularly express their frustration with it, and some people claim that it is no longer funny. (But it is a German joke, so maybe it never was funny.) Anyway: the “tba” should not surprise anyone.


Erdős-Ko-Rado Theorems for Spherical Buildings

Today’s topic combines three of my favorite subjects: Erdős-Ko-Rado theorems (EKR theorems), finite buildings and spectral techniques. All of these topics deserve their own books (and have them, here some examples which I read: Erdos-Ko-Rado Theorems: Algebraic Approaches by Chris Godsil and Karen Meagher, Spectra of Graphs by Andries E. Brouwer and Willem H. Haemers, The Structure of Spherical Buildings by Richard M. Weiss), so I will only touch these topics slightly.

My main aim is to present a variation of the EKR theorem which is motivated by questions about spherical buildings. The variation was recently formulated by Klaus Metsch, Bernhard Mühlherr, and me. If you already know spherical buildings, then you might prefer to read the introduction of our paper instead. (more…)