EAN: 9783110451351

SPACE - TIME - MATTER GEBUNDEN

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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