The stable -algebra of a Smale space is obtained from the étale groupoid associated to the space’s stable equivalence relation. When the original system is mixing, the stable -algebra is simple, separable, nuclear and stably finite. I will outline the construction of an explicit inductive-limit decomposition of the stable -algebra when the stable sets are totally disconnected. From this, one can often compute the -theory of the stable -algebra. The talk will be example-based. In particular, no knowledge of Smale spaces is required. This talk is based on joint work with Allan Yashinski.
(Joint with Anna Puskas) In this talk, we determine all of the imaginary -quadratic fields with class number dividing 32, ; results for were previously computed by Watkins. Our results provide techniques to find complete lists of imaginary -quadratic fields of class number for nonnegative integers . Further, given a fixed we find a bound on for which there are no imaginary -quadratic fields of class number whenever .
I will describe results obtained in collaboration with the Blue Brain Project on the topological analysis of the structure and function of digitally reconstructed microcircuits of neurons in the rat cortex.
I will explain the construction of a new model for the configuration space of a product of two closed manifolds in terms of the configuration spaces of each factor separately. The key to the construction is the lifted Boardman-Vogt tensor product of modules over operads, developed earlier in joint work with Dwyer.