Space - time - matter

More about the book

This monograph presents significant findings from mathematicians and physicists involved in the CRC 647 “Space – Time – Matter” from 2005 to 2016. It focuses on the mathematical and physical foundations of string and quantum field theory, as well as cosmology. Key topics include the spaces and metrics that model the geometry of matter and their evolution. The text delves into the partial differential equations that govern these structures, exploring their singularities, special solutions, and stability properties. The contents cover a range of subjects, including algebraic K-theory, assembly maps, controlled algebra, and trace methods. It discusses Lorentzian manifolds with special holonomy, contributions to the spectral geometry of locally homogeneous spaces, and conformally covariant differential operators related to the holographic Laplacian. Other topics include moduli and deformations, vector bundles in algebraic geometry, Dyson–Schwinger equations for quantum fields, and hidden structures in the form factors of N = 4 SYM. The work also addresses constraints on CFT observables from the bootstrap program, simplifications in amplitudes for various supergravities, Yangian symmetry in maximally supersymmetric Yang-Mills theory, and geometric analysis on singular spaces, including singularities and long-time behavior in nonlinear evolution equations and general relativity.