The Theory of *Quantum Fields* is of great importance for gaining deeper insight into the fundamental laws of nature and has an increasing impact on novel applications. Quantum fields successfully describe the fundamental interactions in elementary particle physics and are of utmost importance for theories beyond the standard model. At the same time the theory of quantum fields plays an increasingly important role in micro- and nano-technology and is an indispensable tool to study phase transitions in many-body systems. On large scales the universal gravitational force described by the *Gravitational Field* dominates. Through the burgeoning field of gravitational wave astronomy with its far reaching implications for astrophysics and cosmology, a deeper knowledge of realistic solutions of the Einstein field equations is urgently needed.

Research in Field Theory profits considerably from mathematical methods and the interdependency of physics and mathematics. For example, the methods from modern Differential Geometry are needed for solving and investigating nonlinear field equations. Ansaetze and thereby emerging integrable structures are at the interface between Field Theory and Differential Geometry. At the same time numerical and stochastic methods become increasingly important, for example in simulations of quantum field theories in elementary-particle and solid-state physics.

Theoretical Physics and Applied Mathematics are main areas of research at the Friedrich-Schiller-University Jena. Our hiring policy has strengthened the areas of *Numerical Relativity, Quantum Field Theory* and *Differential Geometry* considerably. By combining the research competence of the applicants, as for example documented by their active involvement in three DFG Collaborative Research Centres and one DFG Priority Program an attractive and internationally visible graduate center should emerge. For that purpose we offer a well-structured and research-oriented schedule of lecture courses and seminars on specialized topics, regular workshops, internal meetings and a program of international visitors and exchange opportunities. Partners from various Universities have agreed to cooperate with the graduate centre and to help with the training of the students. This will be achieved by hosting some of the graduate students, by advising them or by offering special lectures.