Solving a conjecture of Hopkins and Mahowald, the second author [Ri] showed that Mitchell’s [Mi3] filtration {Fn,k}k=1 of ΩSU(n) splits stably, analogous to the Snaith [Sn2] splitting of BU . Crabb and Mitchell [C-M] then gave similar splittings of ΩU(n)/O(n) and ΩU(2n)/Sp(n). The first filtration Fn,1 is the inclusion CPn−1 ⊂ ΩSU(n), which was actually known to split off by the work of James [...

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The theory of canonical heights on abelian varieties originated with the work of Néron [10] and Tate (first described in print by Manin [8]) in 1965. Tate’s simple and elegant limit construction uses a Cauchy sequence telescoping sum argument. Néron’s construction, which is via more delicate local tools, has proven to be fundamental for understanding the deeper properties of the canonical heigh...

The paper describes an approach that may lead to a proof that the Birch and Swinnerton-Dyer conjecture fails.

In this paper we examine diierences between the two standard methods for computing the 2-Selmer group of an elliptic curve. In particular we focus on practical diierences in the timings of the two methods. In addition we discuss how to proceed if one fails to determine the rank of the curve from the 2-Selmer group. Finally we mention brieey ongoing research i n to generalizing such methods to t...

For many low-resource languages, spoken language resources are more likely to be annotated with translations than with transcriptions. Translated speech data is potentially valuable for documenting endangered languages or for training speech translation systems. A first step towards making use of such data would be to automatically align spoken words with their translations. We present a model ...