 SYMMETRY IN NEWCASTLE
 Location: Room US321, (Callaghan Campus) The University of Newcastle
 Dates: 12:00 pm, Fri, 4^{th} Mar 2022  5:00 pm, Fri, 4^{th} Mar 2022
 Speaker: Dr Michal Ferov, CARMA, The University of Newcastle
 Title: Automorphism groups of Cayley graphs of Coxeter groups: when are they discrete?
Group of automorphisms of a connected locally finite graph is naturally a totally disconnected locally compact topological group, when equipped with the permutation topology. It therefore makes sense to ask for which graphs is the topology not discrete. We show that in case of Cayley graphs of Coxeter groups, one can fully characterise the discrete ones in terms of the symmetries of the corresponding Coxeter system. Joint work with Federico Berlai.
 Speaker: Dr Jeroen Schillewaert, Department of Mathematics, The University of Auckland
 Title: The geometries of the FreudenthalTits magic square
I will give an overview of a programme investigating projective embeddings of (exceptional) geometries which Hendrik Van Maldeghem and I started in 2010.
 Speaker: A/Prof James Parkinson, The University of Sydney
 Title: Automorphisms and opposition in spherical buildings
The geometry of elements fixed by an automorphism of a spherical building is a rich and wellstudied object, intimately connected to the theory of Galois descent in buildings. In recent years, a complementary theory has emerged investigating the geometry of elements mapped onto opposite elements by a given automorphism. In this talk we will give an overview of this theory. This work is joint primarily with Hendrik Van Maldeghem (along with others).
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