A new characterization of the exceptional Lie algebras

For a simple Lie algebra, over $\mathbb{C}$, we consider the weight which is the sum of all simple roots and denote it $\tilde{\alpha}$. We formally use Kostant's weight multiplicity formula to compute the "dimension" of the zero-weight space. In type $A_r$, $\tilde{\alpha}$ is the highest root, and therefore this dimension is the rank of the Lie algebra. In type $B_r$, this is the defining representation, with dimension equal to 1. In the remaining cases, the weight $\tilde{\alpha}$ is not dominant and is not the highest weight of an irreducible finite-dimensional representation. Kostant's weight multiplicity formula, in these cases, is assigning a value to a virtual representation. The point, however, is that this number is nonzero if and only if the Lie algebra is classical. This gives rise to a new characterization of the exceptional Lie algebras as the only Lie algebras for which this value is zero.Comment: 22 pages, 2 figures, and 8 table

Bounds of the rank of the Mordell-Weil group of jacobians of hyperelliptic curves

In this article we extend work of Shanks and Washington on cyclic extensions, and elliptic curves associated to the simplest cubic fields. In particular, we give families of examples of hyperelliptic curves $C: y^2=f(x)$ defined over $\mathbb{Q}$, with $f(x)$ of degree $p$, where $p$ is a Sophie Germain prime, such that the rank of the Mordell--Weil group of the jacobian $J/\mathbb{Q}$ of $C$ is bounded by the genus of $C$ and the $2$-rank of the class group of the (cyclic) field defined by $f(x)$, and exhibit examples where this bound is sharp.Comment: 22 pages, To appear in J. Th\'eor. Nombres Bordeau

About Telling: Ghosts and Hauntings in Contemporary Drama and Poetry

It is difficult to think of something as formally resistant to definition as a ghost. What is more ambiguous than something described as “haunting”? Few currents in literature have been as prominent – and as comparatively unremarked – as the current critical and literary dependence on the language of spectrality. While ghost stories in prose have gained substantial attention, in drama and poetry ghosts and hauntings have found less critical purchase. In response, this dissertation takes up a selection of drama and poetry from Ireland, South Africa, and the Caribbean to illustrate the theoretical and critical potential of ghosts and ghost stories in twentieth-century Anglophone world literatures. Selections are picked for their illustrative potential and thematic richness. The constellation of texts articulate a dazzling range of ghosts and ghost stories used creatively to reflect deep investigations and critical awarenesses of metaphors of haunting in epistemological and literary discourses. The first half of “About Telling” examines ghost stories as performances on the theatrical stage to ask questions of relation and narrative (in Conor McPherson’s The Weir), nation and song (in Marina Carr’s By the Bog of Cats…), globalizing technologies and economic change (in Athol Fugard, John Kani, and Winston Ntshona’s Sizwe Banzi is Dead), theatre as technology (in Samuel Beckett’s Shades trilogy) and, finally, mourning and the lament (in J.M. Synge’s Riders to the Sea and Derek Walcott’s The Sea at Dauphin). Each chapter takes up a re-envisioned relationship between drama, narrative, and ghosts. The second half of “About Telling” turns to poetry and questions of lyric theory: tradition and spectropoetics (in Eavan Boland), gothic prosopopoeia (in Breyten Breytenbach), lyric experimentation (in Samuel Beckett), and ekphrastic addresses (in the discrete responses of David Dabydeen and NourbeSe Philip) to the history of the Zong. Once decreated, poetry’s intense pressure on meaning-making in language reveals not stories but ghosts themselves. Refusing transcendental definitions of ghosts and hauntings, this dissertation suggests that the manifold significance of terms such as “ghosts” and “haunting” can organize formal readings of poetry and drama in a recognizable heuristic. In short, language affords the resources for ghosts to enter and survive in our world

Mutations in synaptojanin disrupt synaptic vesicle recycling

Journal ArticleSynaptojanin is a polyphosphoinositide phosphatase that is found at synapses and binds to proteins implicated in endocytosis. For these reasons, it has been proposed that synaptojanin is involved in the recycling of synaptic vesicles. Here, we demonstrate that the unc-26 gene encodes the Caenorhabditis elegans ortholog of synaptojanin. unc-26 mutants exhibit defects in vesicle trafficking in several tissues, but most defects are found at synaptic termini