Christian Bär

Joachim Lohkamp

Matthias Schwarz

This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.

Global Differential Geometry

Reinier Boon

Bernhard Johannes Haubner

Non-coding RNA as Therapeutic Target: A Game Changer in Cardiac Regenerative Strategies?

Thomas Grädler

Robert Mayr

Dieses Beitragswerk bringt Vorreiter, öffentliche Meinungsbildner und renommierte Fachexperten zu Fragestellungen des digitalen Wandels zusammen und bündelt deren Blickwinkel auf dieses entscheidende Zukunftsthema. Somit beleuchten die hochkarätigen Autoren aus Politik, Wirtschaft, Wissenschaft und Recht mit ihren Beiträgen, in zwei Bänden des Herausgeberwerkes, unterschiedliche Facetten der Digitalisierung. Dabei wird bewusst kein abschließendes, wertendes Fazit vorweggenommen – gerade die durchaus kontroversen Sichtweisen der Autoren tragen zum Mehrwert des vorliegenden Werkes und insbesondere der gesellschaftlichen Diskussion zum digitalen Wandel bei.

1. Band: Politik und Wirtschaft

Digitalisierung im Spannungsfeld von Politik, Wirtschaft, Wissenschaft und Recht

This easy-to-read introduction takes the reader from elementary problems through to current research. Ideal for courses and self-study.

Elementary Differential Geometry

Christian Becker

Providing a systematic introduction to differential characters as introduced by Cheeger and Simons, this text describes important concepts such as fiber integration, higher dimensional holonomy, transgression, and the product structure in a geometric manner. Differential characters form a model of what is nowadays called differential cohomology, which is the mathematical structure behind the higher gauge theories in physics.

Differential Characters

Frank Pfäffle

Nicolas Ginoux

This book provides a detailed introduction to linear wave equations on Lorentzian manifolds (for vector-bundle valued fields). After a collection of preliminary material in the first chapter, one finds in the second chapter the construction of local fundamental solutions together with their Hadamard expansion. The third chapter establishes the existence and uniqueness of global fundamental solutions on globally hyperbolic spacetimes and discusses Green's operators and well-posedness of the Cauchy problem. The last chapter is devoted to field quantization in the sense of algebraic quantum field theory. The necessary basics on $C^*$-algebras and CCR-representations are developed in full detail. The text provides a self-contained introduction to these topics addressed to graduate students in mathematics and physics. At the same time, it is intended as a reference for researchers in global analysis, general relativity, and quantum field theory.

Christian Bär

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