Facing South

The idea and the reality of the Global South represent different types of epistemological challenges to the disciplinary identity of comparative (constitutional) law. Taking the Global South seriously in and for comparative constitutional law must mean transcending its use as either a mere marker of supressed difference or a critical wedge against the hegemony of Western/modern constitutional concepts. The Global South must, instead, be unlocked as the real locus—not in a geographical but in a cognitive sense—of constitutional modernity the world over. Such an agenda of epistemic meridianization requires a number of methodological moves, the most important of which is the de-Weberianization of the fundamental terms and normative ideals of comparative constitutional law. De-Weberianization through a Southern lens is not limited to an ideology critique of Western modernity, but is a project to provide a more realist vision of that modernity and, thereby, a deeper understanding of ‘how the world works’ across North and South. A fundamental openness to alterity, hybridity, and contingency as the structural determinants of ‘law in practice’ is what is at the basis of the South and what enables the re-cognition of the modern world in its likeness.

Monodromy and K-theory of Schubert curves via generalized jeu de taquin

International audience We establish a combinatorial connection between the real geometry and the K-theory of complex Schubert curves Spλ‚q, which are one-dimensional Schubert problems defined with respect to flags osculating the rational normal curve. In a previous paper, the second author showed that the real geometry of these curves is described by the orbits of a map ω on skew tableaux, defined as the commutator of jeu de taquin rectification and promotion. In particular, the real locus of the Schubert curve is naturally a covering space of RP1, with ω as the monodromy operator.We provide a fast, local algorithm for computing ω without rectifying the skew tableau, and show that certain steps in our algorithm are in bijective correspondence with Pechenik and Yong's genomic tableaux, which enumerate the K-theoretic Littlewood-Richardson coefficient associated to the Schubert curve. Using this bijection, we give purely combinatorial proofs of several numerical results involving the K-theory and real geometry of Spλ‚q.

Do Brain Decoders Have an Ontological Mind of Their Own? Response to Nikolas Rose

In a recent article published in Body & Society, Nikolas Rose considers what he takes to be possible historical–ontological implications of recent developments in brain-decoding technologies. He argues that such technologies embody the premise that the brain is the real locus of mental states and processes, hence that a new materialist ontology of thought may be in the process of emerging through technological demonstration rather than through philosophical resolution. In this reply, I offer some reasons for being sceptical about such claims. I argue that the ontology in question hardly amounts to anything particularly new, that technologies cannot demonstrate anything in these matters independently of philosophical inclinations of some kind and that it is at least an open issue whether the ontology in question can secure its claim to be a materialist ontology of thought.

A recursion for counts of real curves in ℂℙ2n−1: Another proof

In a recent paper, we obtained a WDVV-type relation for real genus 0 Gromov–Witten invariants with conjugate pairs of insertions; it specializes to a complete recursion in the case of odd-dimensional projective spaces. This paper provides another, more complex-geometric, proof of the latter. The main part of this approach readily extends to real symplectic manifolds with empty real locus, but not to the general case.

Jeremy Belknap’s History of New Hampshire in Context: Settler Colonialism and the Historiography of New England

This essay is a contextual analysis of the History of New Hampshire (1784–1792) by Jeremy Belknap, founder of the Massachusetts Historical Society. I situate Belknap’s historical and institutional achievements within the framework of settler colonialism studies to argue that Belknap used his profound knowledge of previous New England historiography to write a settler history of American colonization—a narrative of expansionist settlement over indigenous land sustained by cultural, political, racial and social norms at the root of its enduring success. Belknap’s settler history effectively negated both British and indigenous sovereignty and shifted the historical focus prevalent in his time away from the empire and onto the specific, and in his mind, unique, story of the violent formation of white, self-governing and autonomous expansionist settler societies that he believed were the real locus of American identity.

EXPECTED TOPOLOGY OF RANDOM REAL ALGEBRAIC SUBMANIFOLDS

Let$X$be a smooth complex projective manifold of dimension$n$equipped with an ample line bundle$L$and a rank$k$holomorphic vector bundle$E$. We assume that$1\leqslant k\leqslant n$, that$X$,$E$and$L$are defined over the reals and denote by$\mathbb{R}X$the real locus of$X$. Then, we estimate from above and below the expected Betti numbers of the vanishing loci in$\mathbb{R}X$of holomorphic real sections of$E\otimes L^{d}$, where$d$is a large enough integer. Moreover, given any closed connected codimension$k$submanifold${\it\Sigma}$of$\mathbb{R}^{n}$with trivial normal bundle, we prove that a real section of$E\otimes L^{d}$has a positive probability, independent of$d$, of containing around$\sqrt{d}^{n}$connected components diffeomorphic to${\it\Sigma}$in its vanishing locus.

HERMITIAN–EINSTEIN CONNECTIONS ON PRINCIPAL BUNDLES OVER FLAT AFFINE MANIFOLDS

Let M be a compact connected special flat affine manifold without boundary equipped with a Gauduchon metric g and a covariant constant volume form. Let G be either a connected reductive complex linear algebraic group or the real locus of a split real form of a complex reductive group. We prove that a flat principal G-bundle EG over M admits a Hermitian–Einstein structure if and only if EG is polystable. A polystable flat principal G-bundle over M admits a unique Hermitian–Einstein connection. We also prove the existence and uniqueness of a Harder–Narasimhan filtration for flat vector bundles over M. We prove a Bogomolov type inequality for semistable vector bundles under the assumption that the Gauduchon metric g is astheno-Kähler.

The Optimization Design of the Pressure Foot Mechanism in a Single-Sheet Feeder

Based on the analysis of the working principle of the pressure foot (the cam- linkage compound mechanism) in a single-sheet feeder, using VB to develop the design of cam mechanism, a mathematical model of optimization design is set-up in which the object function is the minimum deviation between the real locus of the pressure foot and the required locus. The resolving method for this model is also studied with one real example. It is practically valuable.

Geometrically rational real conic bundles and very transitive actions

In this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real algebraic models of compact surfaces: these applications yield new insight into the geometry of the real locus, proving several surprising facts on this geometry. This geometry can be thought of as a half-way point between the biregular and birational geometries.