Syllabus for Math 8851, Fall 2012. Expander graphs and linear groups

TuTh 2-3:15 pm, Kerchof 128.

The course will be somewhat non-standard both in terms of The course will consist of three main parts:

A.  Brief introduction to linear groups (5 weeks)
B.  Introduction to expander graphs (6 weeks)
C.  Linear groups and expander graphs (2 weeks)

The first two parts will be almost unrelated, while the third part will use results and techniques from the first two.

In the first part we will discuss some classical results about the structure theory of linear groups and develop necessary background for the third part of the course. There is no specific text suggested for the first part.

On the contrary, in the second part we will follow quite closely the book Expander Families and Cayley Graphs: A Beginner's Guide by Krebs and Shaheen. The plan is that material in the second part will be presented by students taking (or sitting in) the course, with each student presenting one chapter of the book in two consecutive classes, over the span of six weeks. For this reason you should start reading the book at the very beginning of the fall term and make decisions about what you would like to present by the middle of September. We will start discussing expander graphs after the Fall break and probably cover chapters 1,3,4,5,7 and 8 of the book.

In the third part of the course I hope to talk about some recent work on expansion in linear groups. A more precise plan for this part and suggested references will be announced later in the term.

Getting credit.

If you are officially registered for the course, in order to get credit you must do at least one of the following: These are minimal requirements, and students are encouraged to do both (a) and (b). This applies not only to students registered for the course, but also to those just attending.