Abstract
In this lecture, I will survey several recent results in the local theory of generalized quadrangles. Starting with a short introduction to the global automorphism theory, I will motivate as such the local viewpoint, and overview some of the most important local properties which are investigated nowadays. Recent results on skew translation quadrangles and forms will be described, including a solution of a question of Payne which generalizes work of Havas et al. (Finite geometries, groups, and computation, 2006; Adv Geom 26:389–396, 2006), and then I will mention parts of a classification of skew translation quadrangles which is being prepared by the author. Finally, I will consider conditions which are both global and local.
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