CARMA Seminar

4:00 pm

Tuesday, 19th Nov 2019

SR202, SR Building

James Evans

(University of Western Australia)

Generalised Polygons and their Symmetries

Generalised polygons were first introduced by Jacque Tits in 1959, in the context of studying geometric realisations of the finite simple groups of Lie type. Thus, the study of their symmetry groups and symmetry properties is a rich area of research. My work has focused on studying the point-primitive quadrangles. In my talk I will describe a computer program for testing whether a particular group can act point-primitively on a generalised quadrangle and its application to analysing the almost simple sporadic groups. My work on this program motivated the discovery of a new result dubbed the Line Orbit Lemma, which in turn inspired the conjecturing of the Hemisystem Conjecture, both of which could prove very useful in the analysis of point-primitive quadrangles.