Embeddings of homogeneous spaces in prime characteristics

Let $G$ be a reductive linear algebraic group. The simplest example of a projective homogeneous $G$-variety in characteristic $p$, not isomorphic to a flag variety, is the divisor $x_0 y_0^p+x_1 y_1^p+x_2 y_2^p=0$ in $P^2\times P^2$, which is $SL_3$ modulo a non-reduced stabilizer containing the upper triangular matrices. In this paper embeddings of projective homogeneous spaces viewed as $G/H$, where $H$ is any subgroup scheme containing a Borel subgroup, are studied. We prove that $G/H$ can be identified with the orbit of the highest weight line in the projective space over the simple $G$-representation $L(\lambda)$ of a certain highest weight $\lambda$. This leads to some strange embeddings especially in characteristic $2$, where we give an example in the $C_4$-case lying on the boundary of Hartshorne's conjecture on complete intersections. Finally we prove that ample line bundles on $G/H$ are very ample. This gives a counterexample to Kodaira type vanishing with a very ample line bundle, answering an old question of Raynaud.Comment: 10 pages, AMS-LaTe

Adding fuel to the flames: how TTIP reinvigorated the politicization of trade

It is a truism to state that the Transatlantic Trade and Investment Partnership (TTIP) is a politicized issue, yet the explanations that account for this politicization are mostly singular in nature. In this paper I add to this understanding theoretically and empirically by presenting a broad analytic framework that puts TTIP at the intersection of two evolutions. There is, firstly, a longer-term trend of increasing political authority of (European) trade policy that is (at least by several organizations and citizens) not considered legitimate. I argue that TTIP is an extension and an intensification of this perceived authority-without-legitimacy trend. Secondly, the particular explosive situation that has occurred since 2013 is furthermore the result of a specific combination of a favoring political opportunity structure, combined with pre-existing mobilization resources that have facilitated a large mobilization by civil society organizations. This explains the spike of politicization that is attached onto this longer term trend. Relying on several exploratory interviews, I try to uncover the determinants in the different categories

Batalin-Vilkovisky algebra structures on (Co)Tor and Poisson bialgebroids

In this article, we extend our preceding studies on higher algebraic structures of (co)homology theories defined by a left bialgebroid (U,A). For a braided commutative Yetter-Drinfel'd algebra N, explicit expressions for the canonical Gerstenhaber algebra structure on Ext_U(A,N) are given. Similarly, if (U,A) is a left Hopf algebroid where A is an anti Yetter-Drinfel'd module over U, it is shown that the cochain complex computing Cotor_U(A,N) defines a cyclic operad with multiplication and hence the groups Cotor_U(A,N) form a Batalin-Vilkovisky algebra. In the second part of this article, Poisson structures and the Poisson bicomplex for bialgebroids are introduced, which simultaneously generalise, for example, classical Poisson as well as cyclic homology. In case the bialgebroid U is commutative, a Poisson structure on U leads to a Batalin-Vilkovisky algebra structure on Tor_U(A,A). As an illustration, we show how this generalises the classical Koszul bracket on differential forms, and conclude by indicating how classical Lie-Rinehart bialgebras (or, geometrically, Lie bialgebroids) arise from left bialgebroids.Comment: 37 pages; minor revision (v3: added table of contents), to appear in J. Pure Appl. Algebr

Farming the future

The sustainable production of high quality food, reducing dependency on high energy inputs, improving environmentaland nature conservation, climate change adaptation, animalwelfare and rural livelihoods, are all important challenges faced byEuropean agriculture which can be addressed through organicagricultural practices. However, while the sector has grown dramatically in recent times,much more research needs to be done for this innovative field to come to realise its true potential. As such, the CORE Organic II ERA-Net aims at an effective and sustainable transnational researchprogramme, and has identified common research priorities for the organic sector where a transnational approach will give added value, has initiated research projects, and is organising project monitoring and the dissemination of results. PEN asked Dr Niels Halberg, director of the International Centre for Research in Organic Food Systems (ICROFS) and co-ordinator of the CORE Organic II ERA-Net about the benefits the initiative can bring, the project selection process, and his views on the future of organic agriculture research funding, both at a European and national level

Deriving the Gross-Pitaevskii equation

In experiments, Bose-Einstein condensates are prepared by cooling a dilute Bose gas in a trap. After the phase transition has been reached, the trap is switched off and the evolution of the condensate observed. The evolution is macroscopically described by the Gross-Pitaevskii equation. On the microscopic level, the dynamics of Bose gases are described by the $N$-body Schr\"odinger equation. We review our article [BdS12] in which we construct a class of initial data in Fock space which are energetically close to the ground state and prove that their evolution approximately follows the Gross-Pitaevskii equation. The key idea is to model two-particle correlations with a Bogoliubov transformation.Comment: 5 pages; contribution to the proceedings of QMath1

Density of quasismooth hypersurfaces in simplicial toric varieties

This paper investigates the density of hypersurfaces in a projective normal simplicial toric variety over a finite field having a quasismooth intersection with a given quasismooth subscheme. The result generalizes the formula found by B. Poonen for smooth projective varieties. As an application, we further analyze the density of hypersurfaces with bounds on their number of singularities and on the length of their singular schemes.Comment: extended and accepted versio