David Drake will conduct research into combinatorial problems in geometry. The motivating problem for this work is the long standing conjecture that there are no finite projective planes of non-prime order. Numerous composite orders are well known not to be possible orders but the question remains open even for relatively small numbers such as 10, 12 and 15. Drake will employ computational techniques to make progress with some of these questions. He will investigate the possibility of embedding into finite projective planes certain linear spaces. The objective is to make these embeddings as tight as possible in the sense of minimizing the order of the containing plane. The tightest possible situation would yield planes of non-prime order. In other situations important information in extremal set theory should be forthcoming.
