Classification of span-symmetric generalized quadrangles of order .
The classification of generalized quadrangles with two translation points.
Finite projective planes, Fermat curves, and Gaussian periods
One of the oldest and most fundamental problems in the theory of finite projective planes is to classify those having a group which acts transitively on the incident point-line pairs (flags). The conjecture is that the only ones are the Desarguesian projective planes (over a finite field). In this paper, we show that non-Desarguesian finite flag-transitive projective planes exist if and only if certain Fermat surfaces have no nontrivial rational points, and formulate several other equivalences involving...
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