First of all, apologies to the small number of people who have been reading the posts about the “central amenability constant” of a finite group. When I started the sequence of posts, the goal was to force myself past a certain amount of writer’s block, in the hope that this would help to get a preprint written up. Since then there have been some fairly significant changes in my working life — not least a change of jobs and change of continent — and also various other research projects have had to take priority.
Indeed, the result that I hoped to present in this sequence of blog posts can now be found on the arXiv at
[1410.5134] A gap theorem for the ZL-amenability constant of a finite group
Nevertheless, I still think it may be worthwhile to resume the sequence of posts in the New Year. Rather than serving as a practice run for a preprint, they will instead take the opportunity to be more discursive and explanatory. In particular, I want to try and motivate some of the calculations rather than just stating and proving the theorems, and perhaps include a few more explicit examples.
The other vague project for the New Year is to do some blogging about Banach algebras. Here, the maxims will be: a Banach algebra usually looks nothing like a C*-algebra; and a Banach algebra usually looks nothing like an L1-group algebra. The world of Banach algebras can be much stranger and, for me at least, much richer.