** "Geometry and Analysis on Groups" Research Seminar **

**Time:** 2018.06.12, 15:00–17:00

**Location:** Seminarraum 10, Oskar-Morgenstern-Platz 1, 2.Stock

**Title:** "Subgroups of Thompson's group."

**Speaker:** Justin Moore
(Cornell University)

**Abstract:**
Matthew Brin and Mark Sapir have conjectured that every subgroup of
Thompson's group \(F\) is either elementary amenable or else contains
an isomorphic copy of \(F\).
We hope to address this question by attempting to classify - or at
least better understand - the class of all finitely generated
subgroups of \(F\) up to biembeddability.
In particular, it seems necessary to obtain a more complete
understanding of the elementary amenable subgroups of \(F\) before
attempting to prove the Brin-Sapir conjecture.
We will show that there is a family of finitely generated elementary
amenable subgroups of \(F\) which is strictly well ordered in type
\(\epsilon_0\) by the embeddability relation.
Moreover, we show that the EA-class of a finitely generated subgroup
of \(F\) can be made arbitrarily large below \(\epsilon_0\), improving
on previous results of Brin.
The work presented in this talk is joint with Collin Bleak and Matthew Brin.
The first lecture will develop a language which allows us to specify
certain subgroups of Thompson's group.
The second lecture will focus on the construction of the specific family of examples mentioned above.