Computation of the unipotent Albanese map on elliptic and hyperelliptic curves

We study the unipotent Albanese map appearing in the non-abelian Chabauty method of Minhyong Kim. In particular we explore the explicit computation of the p-adic de Rham period map $$j^{dr}_n$$ j n dr on elliptic and hyperelliptic curves over number fields via their universal unipotent connections $${\mathscr {U}}$$ U . Several algorithms forming part of the computation of finite level versions $$j^{dr}_n$$ j n dr of the unipotent Albanese maps are presented. The computation of the logarithmic extension of $${\mathscr {U}}$$ U in general requires a description in terms of an open covering, and can be regarded as a simple example of computational descent theory. We also demonstrate a constructive version of a lemma of Hadian used in the computation of the Hodge filtration on $${\mathscr {U}}$$ U over affine elliptic and odd hyperelliptic curves. We use these algorithms to present some new examples describing the co-ordinates of some of these period maps. This description will be given in terms iterated p-adic Coleman integrals. We also consider the computation of the co-ordinates if we replace the rational basepoint with a tangential basepoint, and present some new examples here as well.

Which way to the dawn of speech?: Reanalyzing half a century of debates and data in light of speech science

Recent articles on primate articulatory abilities are revolutionary regarding speech emergence, a crucial aspect of language evolution, by revealing a human-like system of proto-vowels in nonhuman primates and implicitly throughout our hominid ancestry. This article presents both a schematic history and the state of the art in primate vocalization research and its importance for speech emergence. Recent speech research advances allow more incisive comparison of phylogeny and ontogeny and also an illuminating reinterpretation of vintage primate vocalization data. This review produces three major findings. First, even among primates, laryngeal descent is not uniquely human. Second, laryngeal descent is not required to produce contrasting formant patterns in vocalizations. Third, living nonhuman primates produce vocalizations with contrasting formant patterns. Thus, evidence now overwhelmingly refutes the long-standing laryngeal descent theory, which pushes back “the dawn of speech” beyond ~200 ka ago to over ~20 Ma ago, a difference of two orders of magnitude.

Descent and Galois theory for Hopf categories

Descent theory for linear categories is developed. Given a linear category as an extension of a diagonal category, we introduce descent data, and the category of descent data is isomorphic to the category of representations of the diagonal category, if some flatness assumptions are satisfied. Then Hopf–Galois descent theory for linear Hopf categories, the Hopf algebra version of a linear category, is developed. This leads to the notion of Hopf–Galois category extension. We have a dual theory, where actions by dual linear Hopf categories on linear categories are considered. Hopf–Galois category extensions over groupoid algebras correspond to strongly graded linear categories.