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Space – Time – Matter

Analytic and Geometric Structures

Edited by: Jochen Brüning and Matthias Staudacher
With contributions of: Bernold Fiedler, Klaus Ecker, Friederike Dittberner, Christian Bär, Lars Andersson, Jochen Brüning, Dorothee Schüth, Helga Baum, Andreas Juhl, Klaus Altmann, Gavril Farkas, Schmitt Alexander, Björn Andreas, Dirk Kreimer, Dhritiman Nandan, Valentina Fiorini, Pedro Liendo, Marco Chiodaroli, Livia Ferro, Juliette Hell, Marco Varisco, Sebastian Boldt, Gang Yang, Jan Plefka, Bei Francesco, Batu Güneysu, and Ludewig Matthias

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

  • A summary of the research of the SFB Space-Time-Matter
  • Includes recent advances in the mathematical foundations of string theory and cosmology
  • With contributions from renowned institutes s.a. the Max Planck Institute for Gravitational Physics

Author Information

Matthias Staudacher and Jochen Brüning, Humboldt-Universität zu Berlin, Germany.

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Audience: Graduate students and researchers in mathematics and physics.

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