It’s hard enough for one author to write a coherent work; for many authors, even if it’s one and the same topic one might end up with Rashoumon (in the sense of different and contradicting narratives). But, as the Princeton Companion to Mathematics shows, it is possible to have a coherent book with each author writing a chapter, and now geometric group theory has one too.
A new book has just come out, and it’s very good.
Office Hours with a Geometric Group Theorist, Edited by Matt Clay & Dan Margalit, 2017.
An undergraduate student walks into the office of a geometric group theorist, curious about the subject and perhaps looking for a senior thesis topic. The researcher pitches their favourite sub-topic to the student in a single “office hour”.
The book collects together 16 independent such “office hours”, plus two introductory office hours by the editors (Matt Clay and Dan Margalit) to get the student off the ground.
Given the number of authors and the variety of concepts that are presented, trying to assemble such a book would seem a recipe for disaster, but the actual result is a resounding success! The level never flies off into the stratosphere and never becomes patronizingly oversimplified – each office hour is at the right level, and the tone remains informal without being wishy-washy. As the researcher is aiming to hook students on their topic, each office hour provides a nice entry point into its topic, with “next steps” mapped out to help the student on their way.
The voice of the researcher is preserved, which is also nice. Aaron Abrams informs us that Thalia’s hair (presumably his daughter) and challah are both braided, and Johanna Mangahas explains the Ping-pong Lemma using ping-pong.
The greatest highlight of the book is perhaps the exercises, which are pitched at a good introductory level and help the student wrap their brains around the topic.
I think that the book isn’t only a collection of good lead-ins for undergraduates- these “office hours” are equally useful for graduate students and for mathematicians who don’t happen to specialize in those fields, but who want to sightsee some key ideas quickly.
I very highly recommend it!!