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Tuesday, December 01, 2015
3:00 PM - 4:30 PM

Logic Seminar

Automatic continuity notions and locally compact Polish groups
Phillip Wesolek, Professor, Mathematics, Université Catholique de Louvain,

 (Joint with François Le Maître)  Profinite branch groups are a large, interesting family of infinite compact subgroups of automorphism groups of rooted trees. We demonstrate the equivalence of many automatic continuity type properties for these groups. In particular, we show the equivalence of the small index property, the Bergman property, and the condition that every proper normal subgroup is open; groups enjoying the latter condition are called strongly just infinite. Strongly just infinite profinite branch groups with mild additional restrictions are then shown to additionally satisfy the invariant automatic continuity property and the locally compact automatic continuity property. Examples are then presented. As an application, non-discrete simple locally compact Polish groups with the small index property, the invariant automatic continuity property, and the locally compact automatic continuity property are presented.

For more information, please contact Alexander Kechris by email at [email protected] or visit http://www.math.caltech.edu/~logic/index.html.