Kathryn Hess (EPFL) Configuration spaces of products Sponsored by the Meyer Fund

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The stable $C}^{*$-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 $C}^{*$-algebra is simple, separable, nuclear and stably finite. I will outline the construction of an explicit inductive-limit decomposition of the stable $C}^{*$-algebra when the stable sets are totally disconnected. From this, one can often compute the $K$-theory of the stable $C}^{*$-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.

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(Joint with Anna Puskas) In this talk, we determine all of the imaginary $n$-quadratic fields with class number dividing 32, $n>1$; results for $n=1$ were previously computed by Watkins. Our results provide techniques to find complete lists of imaginary $n$-quadratic fields of class number $2}^{m$ for nonnegative integers $m$. Further, given a fixed $m>0$ we find a bound $B(m)$ on $n$ for which there are no imaginary $n$-quadratic fields of class number $2}^{m$ whenever $n>B(m)$.

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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.

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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.