SYMMETRY IN NEWCASTLE Location: Room US321, (Callaghan Campus) The University of Newcastle Dates: 12:00 pm, Fri, 4th Mar 2022 - 5:00 pm, Fri, 4th 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 Freudenthal-Tits 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 well-studied 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). [Permanent link]