Type: Seminar

Distribution: World

Expiry: 21 Nov 2024

CalTitle1: Algebra Seminar: The geometry of conjugation in Euclidean isometry groups

Auth: alexs@w447y6s3.staff.wireless.sydney.edu.au (ashe8718) in SMS-SAML

Anne Thomas (USyd) will be speaking in the algebra seminar next week. We will go out for lunch after the talk. Where: Carslaw 275 When: Friday September 20, 12-1pm Title: The geometry of conjugation in Euclidean isometry groups Abstract: We give a simple and beautiful description of the geometry of conjugation within any split subgroup H of the full isometry group G of Euclidean space. We prove that for any h in H, the conjugacy class [h] is described geometrically by the move-set of its linearisation, while the set of elements conjugating h to a given h’ in [h] is described by the fix-set of its linearisation. Examples include affine Coxeter groups, where we give finer results, certain crystallographic groups, and the group G itself. This is joint work with Elizabeth Mili’cevi’c and Petra Schwer.