Informal Friday Seminar: Thomas -- Bass-Serre theory

This week’s IFS speaker is Anne Thomas, who will give two talks on
Bass-Serre theory, in Carslaw 830 as usual.  

Time and Date: Friday, 26 May and 2 June, 9-11am 

Location: Carslaw 830 and online 

Zoom link: https://uni-sydney.zoom.us/j/84792295528 

Title: Bass-Serre theory 

Abstract: I will introduce the theory of "graphs of groups", which is also known as
"Bass-Serre theory".  This theory was originally developed by Bass and Serre in order to
understand a theorem of Ihara concerning the group SL_2(Q_p), and is now part of the
basic toolkit of geometric group theory and low-dimensional topology.  I will present
both Serre’s treatment of this topic, from Chapter I of his 1977 book "Trees" (title in
French: "Arbres, amalgames, SL_2"), and the topological version developed slightly later
by Scott and Wall.  There will be numerous examples, including important constructions
in combinatorial group theory (free products with amalgamation, HNN extensions) and
important families of groups and their actions on trees (Baumslag-Solitar groups,
SL_2(R) for various rings R).  

Reminder: This semester we will cover several topics in the IFS, spending around two
weeks with every speaker.  As usual, the goal of the seminar is to give the flavour of
the subject, not all the nitty gritty details.  Questions and sidebars are encouraged,
and we’ll emphasise examples, intuition, tools and historical diversions.  The talks
are intended to be conversational, so come ready to engage! The website remains in the
same place: https://sites.google.com/view/ifssydney/home