讲座内容：

Roughlyspeaking, the “Kruskal-Katona-type problem for a graph G”concerned here is todescribe each subset of vertices  of Gthat has minimal neighborhood respect to its size. We establish aKruskal-Katona-type theorem for the q-Kneser graph,whose vertex set consists ofall k-dimensional subspaces of an n-dimensional linear space over a q-elementfield, two subspaces are adjacent if they have the trivial intersection. Itincludes as a special case the Erdos--Ko--Rado theorem for intersectingfamilies in finite vector spaces and yields a short proof of the Hilton-Milner theorem for nontrivial intersectingfamilies in finite vector spaces.