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Independent sets in geometries

Independent sets or cocliques play an important role in graph theory, and finding the maximal size of an independent set for specific classes of graphs is a major research topic. However, for bipartite graphs the standard measure of size for an independent set does not necessarily make a lot of sense, as each of the parts will be an (uninteresting) independent set. A different way to measure how ''large'' an independent set is will be introduced.  Then I will discuss ''large'' independent sets in bipartite graphs from a geometric point of view (after all, every bipartite graph is equivalent to a point-line geometry).