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