Mathematical Sciences: Existence Problems for Projective    Planes and Maximal Cliques
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{'SignBlockName': 'James Glazebrook', 'PO_EMAI': None, 'PO_PHON': None}
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.
{'FirstName': 'David', 'LastName': 'Drake', 'PI_MID_INIT': 'A', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'David A Drake', 'EmailAddress': 'dad@math.ufl.edu', 'NSF_ID': '000275545', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '126500', 'Text': 'GEOMETRIC ANALYSIS'}
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