Mori dream spaces as fine moduli of quiver representations

Mori Dream Spaces and their Cox rings have been the subject of a great deal of interest since their introduction by Hu–Keel over a decade ago. From the geometric side, these varieties enjoy the property that all operations of the Mori programme can be carried out by variation of GIT quotient, while from the algebraic side, obtaining an explicit presentation of the Cox ring is an interesting problem in itself. Examples include Q-factorial projective toric varieties, spherical varieties and log Fano varieties of arbitrary dimension. In this thesis we use the representation theory of quivers to study multigraded linear series on Mori Dream Spaces. Our main results construct Mori Dream Spaces as fine moduli spaces of ϑ-stable representations of bound quivers for a special stability condition ϑ, thereby extending results of Craw–Smith for projective toric varieties

Social representations theory and critical: Constructionism: Insights from Caillaud's article

he aim of this paper is to highlight therole that Social Representations Theory (SRT) could play in the debate on the criticalpotential of social constructionist perspectives. Wedraw upon some of the arguments raised by Caillaud (this issue), mainly concerning such a sensitive topic as environmental issues, to highlightsomecrucial points of that debate. As is well known, one of the goals of the social constructionist movement has been to takea more critical stance towards taken-for-granted knowledge (Gergen,1985; Burr,1995). It aimsto show that our understanding of the world is by no means neutral or value-free;it is instead the result of historical and cultural specificities, which operate ideologically. In this vein, the social constructionist approach raises the question of social transformation and emancipation, as well as the problems of power and social inequality, in close consonance with the scope of the more general critical approach in psychology (Tolman&Maiers, 1991)

Floquet Energies and Quantum Hall Effect in a Periodic Potential

The Quantum Hall Effect for free electrons in external periodic field is discussed without using the linear response approximation. We find that the Hall conductivity is related in a simple way to Floquet energies (associated to the Schroedinger equation in the co-moving frame). By this relation one can analyze the dependence of the Hall conductivity from the electric field. Sub-bands can be introduced by the time average of the expectation value of the Hamiltonian on the Floquet states. Moreover we prove previous results in form of sum rules as, for instance: the topological character of the Hall conductivity (being an integer multiple of e^2/h), the Diofantine equation which constrains the Hall conductivity by the rational number which measures the flux of the magnetic field through the periodicity cell. The Schroedinger equation fixes in a natural way the phase of the wave function over the reduced Brillouin zone: thus the topological invariant providing the Hall conductivity can be evaluated numerically without ambiguity.Comment: LaTex (revtex), 18 pages, 10 figures in .eps using epsf.sty. Changes in eq. (3.2). References adde

Democratic Representations

Minimization of the $\ell_{\infty}$ (or maximum) norm subject to a constraint that imposes consistency to an underdetermined system of linear equations finds use in a large number of practical applications, including vector quantization, approximate nearest neighbor search, peak-to-average power ratio (or "crest factor") reduction in communication systems, and peak force minimization in robotics and control. This paper analyzes the fundamental properties of signal representations obtained by solving such a convex optimization problem. We develop bounds on the maximum magnitude of such representations using the uncertainty principle (UP) introduced by Lyubarskii and Vershynin, and study the efficacy of $\ell_{\infty}$-norm-based dynamic range reduction. Our analysis shows that matrices satisfying the UP, such as randomly subsampled Fourier or i.i.d. Gaussian matrices, enable the computation of what we call democratic representations, whose entries all have small and similar magnitude, as well as low dynamic range. To compute democratic representations at low computational complexity, we present two new, efficient convex optimization algorithms. We finally demonstrate the efficacy of democratic representations for dynamic range reduction in a DVB-T2-based broadcast system.Comment: Submitted to a Journa

Almost Representations and Asymptotic Representations of Discrete Groups

We define for discrete finitely presented groups a new property related to their asymptotic representations. Namely we say that a groups has the property AGA if every almost representation generates an asymptotic representation. We give examples of groups with and without this property. For our example of a group $G$ without AGA the group $K^0(BG)$ cannot be covered by asymptotic representations of $G$.Comment: 9 pages, LaTeX 2.0

Loop Representations

The loop representation plays an important role in canonical quantum gravity because loop variables allow a natural treatment of the constraints. In these lectures we give an elementary introduction to (i) the relevant history of loops in knot theory and gauge theory, (ii) the loop representation of Maxwell theory, and (iii) the loop representation of canonical quantum gravity. (Based on lectures given at the 117. Heraeus Seminar, Bad Honnef, Sept. 1993)Comment: 38 pages, MPI-Ph/93-9

Vector coherent state representations, induced representations, and geometric quantization: I. Scalar coherent state representations

Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced unitary representations corresponding to prequantization; and (iii) irreducible unitary representations obtained in geometric quantization by choice of a polarization. These representations establish an intimate relation between coherent state theory and geometric quantization in the context of induced representations.Comment: 29 pages, part 1 of two papers, published versio