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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 Ï‘-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
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: II. Vector coherent state representations
It is shown here and in the preceeding paper (quant-ph/0201129) that vector
coherent state theory, the theory of induced representations, and geometric
quantization provide alternative but equivalent quantizations of an algebraic
model. The relationships are useful because some constructions are simpler and
more natural from one perspective than another. More importantly, each approach
suggests ways of generalizing its counterparts. In this paper, we focus on the
construction of quantum models for algebraic systems with intrinsic degrees of
freedom. Semi-classical partial quantizations, for which only the intrinsic
degrees of freedom are quantized, arise naturally out of this construction. The
quantization of the SU(3) and rigid rotor models are considered as examples.Comment: 31 pages, part 2 of two papers, published versio
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