# Events for 03/08/2023 from all calendars

## Groups and Dynamics Seminar

**Time: ** 3:00PM - 4:00PM

**Location: ** BLOC 302

**Speaker: **Yaroslav Vorobets

**Title: ***Maximal subgroups of ample (topological full) groups*

**Abstract: **Given a group of homeomorphisms of the Cantor set, usually there are
many ways to construct a new homeomorphism, as a puzzle, from pieces of several
given ones. The group is called ample (or topological full) if it already
contains all homeomorphisms obtained that way.
The talk is concerned with the first attempt at a classification of maximal
subgroups of ample groups. Results that will be presented are mostly parallel to
the classification of maximal subgroups of finite symmetric groups.
Recall that all subgroups of the symmetric group are divided into three
classes: intransitive subgroups (those that leave invariant a nontrivial
subset), imprimitive subgroups (transitive subgroups that leave invariant a nontrivial partition), and primitive subgroups (the remaining ones).
It turns out that the maximal intransitive subgroups are stabilizers of
certain subsets while the maximal imprimitive subgroups are stabilizers
of certain partitions.
In the case of the ample groups, arbitrary subsets and partitions are
replaced by closed subsets and partitions into closed subsets. Transitivity
is replaced by minimality (absence of nontrivial closed invariant subsets).
This is the joint work with Rostislav Grigorchuk.