An AIM workshop on set theory and C*-algebras

Last week I attended a workshop on set theory and C*-algebras at the AIM. Here is how it went…

When you approach the American Institute of Mathematics, you get the distinct impression that you are about to see some seriously low, low prices on mp3 players. The reason for this is that you cannot approach the AIM without approaching a Fry’s Electronics; a discount superstore with a poor ethical history. In fact, the AIM is behind an ill-marked door leading to a windowless cave adjacent to the store. It is a dry office space, filled with books and binders full of dry leaves of aging mathematics. And there is coffee and bagels for breakfast.

Founded by a Mr. John Fry some 20 years ago, the AIM hosts a special workshop in mathematics each week. The format diverges, however, from the usual endless barrage of talks. Instead, there are just a few introductory talks followed by clarification sessions. Later in the week, the questions transition into research questions, with voting to determine which ones to attack, also in small sessions. There are also impromptu talks of a specialized nature when there is sufficient demand.

Last week, the topic was the overlap of set theory and C*-algebras, which is one of my (lately) favorite areas. During the introductory portion of the workshop, I was glad to have the opportunity to become more comfortable working with C*-algebras in general. However, my questions in particular were of a somewhat basic nature, and I found it hard to get such questions answered. My session was half filled with ringers who would push the speaker onward. In this case, I actually would have preferred a more traditional format; perhaps a well-prepared talk just for the non-C*-algebraists, one which methodically addressed a range of basic facts.

One of the most useless moments for me came when I asked a question about dimension in C*-algebras:

Sam: (some question about nuclear C*-algebras)
Self-appointed moderator: (some techno-babble ending with…) Like take a CW complex.
(pause)
Sam: Are you talking to me?

This was followed by general laughter and then wine. It was not followed by an y hint of what is a CW complex, nor of what the heck it has to do with anything said so far this week.

Later in the week, I joined a session which focused on dynamical properties of the automorphism group Aut(A) for some very well behaved algebras A. The goal was to establish one fixed property (namely turbulence, which I’ll hopefully address in a later post), and also to obtain a template for establishing this property for more and more algebras A. Unfortunately, it’s rather difficult to use 13 different humans as problem-solving resources, since for instance they cannot all be kept up to speed all the time. In fact, I was often left behind as the “real” problem-solvers plowed on.

Despite any criticisms, the conference was an overall success for me. First, I did somehow greatly expand my basic understanding of C*-algebras. And second, the problem-solvers failed in the end (ha!), while on the other hand I have very good notes and I can certainly continue working on this and related problems in the future.

I’ll conclude by giving the workshop a letter grade: B