We want to look at spherical diagrams (in particular diagrams of projective spaces for this talk) and we try to find the size of maximum set of particular flags which are mutually not far apart. The meaning of 'being far apart' changes up to the diagram and up to the objects that we pick by cycling the nodes of the diagrams. Indeed, this is a generalization of the problem of finding maximal cocliques in the Kneser graphs. This time the Kneser graphs are defined over the quotients of the Chevalley groups. Here, instead of k-sets, we want flags to be not far apart.
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