258 research outputs found
On quantization of singular varieties and applications to D-branes
We calculate the ring of differential operators on some singular affine
varieties (intersecting stacks, a point on a singular curve or an orbifold).
Our results support the proposed connection of the ring of differential
operators with geometry of D-branes in (bosonic) string theory. In particular,
the answer does know about the resolution of singularities in accordance with
the string theory predictions.Comment: LaTeX2e, 17 pages, misprints correcte
Graded infinite order jet manifolds
The relevant material on differential calculus on graded infinite order jet
manifolds and its cohomology is summarized. This mathematics provides the
adequate formulation of Lagrangian theories of even and odd variables on smooth
manifolds in terms of the Grassmann-graded variational bicomplex.Comment: 30 page
Proof of the Hyperplane Zeros Conjecture of Lagarias and Wang
We prove that a real analytic subset of a torus group that is contained in
its image under an expanding endomorphism is a finite union of translates of
closed subgroups. This confirms the hyperplane zeros conjecture of Lagarias and
Wang for real analytic varieties. Our proof uses real analytic geometry,
topological dynamics and Fourier analysis.Comment: 25 page
On Twistors and Conformal Field Theories from Six Dimensions
We discuss chiral zero-rest-mass field equations on six-dimensional
space-time from a twistorial point of view. Specifically, we present a detailed
cohomological analysis, develop both Penrose and Penrose-Ward transforms, and
analyse the corresponding contour integral formulae. We also give twistor space
action principles. We then dimensionally reduce the twistor space of
six-dimensional space-time to obtain twistor formulations of various theories
in lower dimensions. Besides well-known twistor spaces, we also find a novel
twistor space amongst these reductions, which turns out to be suitable for a
twistorial description of self-dual strings. For these reduced twistor spaces,
we explain the Penrose and Penrose-Ward transforms as well as contour integral
formulae.Comment: v4: 66 pages, typos fixed, appendix B revise
Scaling law in the Standard Map critical function. Interpolating hamiltonian and frequency map analysis
We study the behaviour of the Standard map critical function in a
neighbourhood of a fixed resonance, that is the scaling law at the fixed
resonance. We prove that for the fundamental resonance the scaling law is
linear. We show numerical evidence that for the other resonances , , and and relatively prime, the scaling law follows a
power--law with exponent .Comment: AMS-LaTeX2e, 29 pages with 8 figures, submitted to Nonlinearit
Differential Forms on Log Canonical Spaces
The present paper is concerned with differential forms on log canonical
varieties. It is shown that any p-form defined on the smooth locus of a variety
with canonical or klt singularities extends regularly to any resolution of
singularities. In fact, a much more general theorem for log canonical pairs is
established. The proof relies on vanishing theorems for log canonical varieties
and on methods of the minimal model program. In addition, a theory of
differential forms on dlt pairs is developed. It is shown that many of the
fundamental theorems and techniques known for sheaves of logarithmic
differentials on smooth varieties also hold in the dlt setting.
Immediate applications include the existence of a pull-back map for reflexive
differentials, generalisations of Bogomolov-Sommese type vanishing results, and
a positive answer to the Lipman-Zariski conjecture for klt spaces.Comment: 72 pages, 6 figures. A shortened version of this paper has appeared
in Publications math\'ematiques de l'IH\'ES. The final publication is
available at http://www.springerlink.co
On dilation symmetries arising from scaling limits
Quantum field theories, at short scales, can be approximated by a scaling
limit theory. In this approximation, an additional symmetry is gained, namely
dilation covariance. To understand the structure of this dilation symmetry, we
investigate it in a nonperturbative, model independent context. To that end, it
turns out to be necessary to consider non-pure vacuum states in the limit.
These can be decomposed into an integral of pure states; we investigate how the
symmetries and observables of the theory behave under this decomposition. In
particular, we consider several natural conditions of increasing strength that
yield restrictions on the decomposed dilation symmetry.Comment: 40 pages, 1 figur
Felix Alexandrovich Berezin and his work
This is a survey of Berezin's work focused on three topics: representation
theory, general concept of quantization, and supermathematics.Comment: LaTeX, 27 page
Mouse Embryonic Retina Delivers Information Controlling Cortical Neurogenesis
The relative contribution of extrinsic and intrinsic mechanisms to cortical development is an intensely debated issue and an outstanding question in neurobiology. Currently, the emerging view is that interplay between intrinsic genetic mechanisms and extrinsic information shape different stages of cortical development [1]. Yet, whereas the intrinsic program of early neocortical developmental events has been at least in part decoded [2], the exact nature and impact of extrinsic signaling are still elusive and controversial. We found that in the mouse developing visual system, acute pharmacological inhibition of spontaneous retinal activity (retinal waves-RWs) during embryonic stages increase the rate of corticogenesis (cell cycle withdrawal). Furthermore, early perturbation of retinal spontaneous activity leads to changes of cortical layer structure at a later time point. These data suggest that mouse embryonic retina delivers long-distance information capable of modulating cell genesis in the developing visual cortex and that spontaneous activity is the candidate long-distance acting extrinsic cue mediating this process. In addition, these data may support spontaneous activity to be a general signal coordinating neurogenesis in other developing sensory pathways or areas of the central nervous system
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