At the rate I’ve been writing up this post, I’m surprised I finished it before March. The January Notices of the AMS have been out for a while. The feature article, Homological Sensor Networks, describes an application of homology to network design. I predict computational homology will be a major growth area for applied mathematics in the future.
What is… a projective structure introduces manifolds that are locally modelled after projective space. There’s also a review of Fearless Symmetry, which is a popularization of advanced number theory (going so far as to talk about the relationship between number theory and representations of Galois groups, apparently). My library has this book, so I plan taking a look to see how the authors do.
(The February Notices are already online, but I’ll save a post for that when I finally get a chance to look at it. If the March Notices are already online, I don’t want to know about it.)