I finally had a chance to take a look at the September Notices of the AMS. Allyn Jackson’s Conjectures No More summarizes the conventional wisdom that the PoincarÃ© and Geometrization conjectures are now theorems. What is… a quasicrystal?, by Marjorie Senechal, describes quasicrystals (crystals whose diffraction pattern implies they have symmetries that cannot be explained by a cyrstallographic group) and Penrose tilings.

The feature article, Notes on the Deuring-Heilbronn Phenomenon, by Jeffrey Stopple, discusses some results on Dirichlet L-functions.