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Equivariant cohomology on smooth manifolds is the subject of this
book which is part of a collection of volumes edited by J. Bruning
and V.W. Guillemin. The point of departure are two relatively short
but very remarkable papers be Henry Cartan, published in 1950 in
the Proceedings of the "Colloque de Topologie." These papers are
reproduced here, together with a modern introduction to the
subject, written by two of the leading experts in the field. This
"introduction" comes as a textbook of its own, though, presenting
the first full treatment of equivariant cohomology in the de Rahm
setting. The well known topological approach is linked with the
differential form aspect through the equivariant de Rahm theorem.
The systematic use of supersymmetry simplifies considerably the
ensuing development of the basic technical tools which are then
applied to a variety of subjects, leading up to the localization
theorems and other very recent results."
What is the true mark of inspiration? Ideally it may mean the
originality, freshness and enthusiasm of a new breakthrough in
mathematical thought. The reader will feel this inspiration in all
four seminal papers by Duistermaat, Guillemin and H rmander
presented here for the first time ever in one volume. However, as
time goes by, the price researchers have to pay is to sacrifice
simplicity for the sake of a higher degree of abstraction. Thus the
original idea will only be a foundation on which more and more
abstract theories are being built. It is the unique feature of this
book to combine the basic motivations and ideas of the early
sources with knowledgeable and lucid expositions on the present
state of Fourier Integral Operators, thus bridging the gap between
the past and present. A handy and useful introduction that will
serve novices in this field and working mathematicians equally
well.
Equivariant cohomology on smooth manifolds is the subject of this
book which is part of a collection of volumes edited by J. Bruning
and V.W. Guillemin. The point of departure are two relatively short
but very remarkable papers be Henry Cartan, published in 1950 in
the Proceedings of the "Colloque de Topologie." These papers are
reproduced here, together with a modern introduction to the
subject, written by two of the leading experts in the field. This
"introduction" comes as a textbook of its own, though, presenting
the first full treatment of equivariant cohomology in the de Rahm
setting. The well known topological approach is linked with the
differential form aspect through the equivariant de Rahm theorem.
The systematic use of supersymmetry simplifies considerably the
ensuing development of the basic technical tools which are then
applied to a variety of subjects, leading up to the localization
theorems and other very recent results."
What is the true mark of inspiration? Ideally it may mean the
originality, freshness and enthusiasm of a new breakthrough in
mathematical thought. The reader will feel this inspiration in all
four seminal papers by Duistermaat, Guillemin and H rmander
presented here for the first time ever in one volume. However, as
time goes by, the price researchers have to pay is to sacrifice
simplicity for the sake of a higher degree of abstraction. Thus the
original idea will only be a foundation on which more and more
abstract theories are being built. It is the unique feature of this
book to combine the basic motivations and ideas of the early
sources with knowledgeable and lucid expositions on the present
state of Fourier Integral Operators, thus bridging the gap between
the past and present. A handy and useful introduction that will
serve novices in this field and working mathematicians equally
well.
This monograph describes some of the most interesting results
obtained by the mathematicians and physicists collaborating in the
CRC 647 "Space - Time - Matter", in the years 2005 - 2016. The work
presented concerns the mathematical and physical foundations of
string and quantum field theory as well as cosmology. Important
topics are the spaces and metrics modelling the geometry of matter,
and the evolution of these geometries. The partial differential
equations governing such structures and their singularities,
special solutions and stability properties are discussed in detail.
Contents Introduction Algebraic K-theory, assembly maps, controlled
algebra, and trace methods Lorentzian manifolds with special
holonomy - Constructions and global properties Contributions to the
spectral geometry of locally homogeneous spaces On conformally
covariant differential operators and spectral theory of the
holographic Laplacian Moduli and deformations Vector bundles in
algebraic geometry and mathematical physics Dyson-Schwinger
equations: Fix-point equations for quantum fields Hidden structure
in the form factors ofN = 4 SYM On regulating the AdS superstring
Constraints on CFT observables from the bootstrap program
Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein
supergravities Yangian symmetry in maximally supersymmetric
Yang-Mills theory Wave and Dirac equations on manifolds Geometric
analysis on singular spaces Singularities and long-time behavior in
nonlinear evolution equations and general relativity
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Atlas der Weltbilder (German, Hardcover)
Christoph Markschies, Ingeborg Reichle, Jochen Bruning, Peter Deuflhard; Contributions by Steffen Siegel, …
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R5,939
R5,093
Discovery Miles 50 930
Save R846 (14%)
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Ships in 10 - 15 working days
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Praktiken visueller Welterzeugung in Form von Weltbildern lassen
sich bereits in der Antike beobachten und haben sich bis heute als
Mittel zur Konstruktion von Ordnungsvorstellungen bewahrt. Seit
jeher steht der begrifflichen Ordnung der Welt eine modellhaft
anschauliche Ordnung gegenuber. Die grundlegende Bedeutung, die
Anschaulichkeit fur unser Verstandnis von der Welt spielt und die
die vielfaltigsten Weltbilder hervorgebracht hat, ist jedoch mehr
als eine blosse Wiederholung des Sehens. Die Bildwelten der
Weltbilder geben uns nicht nur ein anschauliches Bild von der Welt
und vom Kosmos. Sie sind zugleich wirkungsmachtige Instrumente zum
praktischen und theoretischen Handeln in der Welt und formen auf
unterschiedlichste Weise unsere Vorstellungen von der Welt und
unsere Weltanschauung. Die grundlegenden Fragen, die dabei gestellt
werden, haben sich durch die Jahrhunderte nicht wirklich geandert.
Sie betreffen die den Menschen umfassende Ordnung und seine
Stellung innerhalb dieser Ordnung: Welche Gestalt hat die Welt?
Welche Krafte und Ideen wirken in ihr? Woraus besteht sie? Wie ist
sie entstanden? Wie sieht ihre Zukunft aus? Bereits die fruhen
Beispiele von Weltbildern machen deutlich, dass die sowohl in
Bildern als auch in Erzahlungen zur Erscheinung gebrachte
Wirklichkeit immer eine vom Menschen hervorgebrachte ist und daher
stets interpretierte Wirklichkeit und symbolische Konstruktion
bedeutet. Die gesammelten Beispiele reprasentieren zugleich
unterschiedliche visuelle Medien, die im Dienst der Konstruktion
der Welt als Bild stehen. Damit ist die Geschichte der Weltbilder
nicht nur eine Geschichte wechselnder Weltvorstellungen, sondern
zugleich auch eine Geschichte wechselnder Darstellungsmethoden und
unterschiedlicher Tragermedien. Der Atlas der Weltbilder behandelt
ein breites Spektrum von Artefakten und schreitet einen grossen
zeitlichen Bogen ab, der mit altorientalischen und altagyptischen
Weltkonzeptionen beginnt und mit aktuellen Simulationen der
Astrophysik endet. Der Atlas der Weltbilder dokumentiert somit
Aspekte der Kulturgeschichte visueller Welterzeugung in Form von
Weltbildern aus den zuruckliegenden zweieinhalb Jahrtausenden.
Paradigmatische Analysen der Prinzipien und Funktionen sowie der
Geschichte und Bedeutung von Weltbildern geben erstmals umfassenden
Aufschluss uber dieses umfangreiche Themengebiet."
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