The Mathematics Department of the Université libre de Bruxelles is proud to announce that
will give a talk on Monday 6th of July at 3pm, Forum A, Campus de la Plaine, Université libre de Bruxelles, entitled
The ubiquity of alternating groups
(as automorphism groups of symmetric structures)
There are several contexts in which finite alter- nating groups occur as the automorphism group (or orientation-preserving automorphism group) of a dis- crete structure with maximum possible symmetry under certain constraints. In fact, it frequently happens that all but finitely many appear in the given context, and sometimes all but finitely many symmetric groups occur as well (or instead).
Examples include Hurwitz surfaces (compact Riemann surfaces of genus with conformal automorphisms), or equivalently, regular maps of type , and also 5-arc-transitive cubic graphs, 7-arc- transitive 4-valent graphs, and hyperbolic 3-manifolds of largest possible symmetry-to-volume ratio.
I will explain some of these, as well as a recent one (locally 9-arc-transitive bipartite graphs), and the possibility that for every , all but finitely many and occur as the automorphism group of a chiral polytope of rank .
Marston D. E. Conder is a Distinguished Professor of the University of Auckland, New Zealand. He is one of the leading mathematicians in his fields of research which include Combinatorial Group Theory and Graph Theory. He obtained his PhD thesis in Oxford in 1980 under the supervision of Graham Higman. He became a Fellow of the American Mathematical Society in 2012.
Marston D. E. Conder is known for his wonderful exposures in favor of audiences including the bachelor students.