**Structure of Local Quantum Field Theories**

**Prof. Dr. Dirk Kreimer (ret.)**

Alexander von Humboldt Chair for Mathematical Physics

My research focuses on the structure of locally interacting quantum fields in four dimensions of spacetime. A major topic is the mathematical structure of renormalization, and the arithmetic properties of the periods which appear in the computation of renormalization group functions, as well as the analytic structure of renormalized amplitudes, with emphasis on monodromy, Cutkosky rules and the scattering matrix. An enormous amount of empirical knowledge is available in physics about these questions. The hope is that connecting it to recent developments in mathematics helps both disciplines, and answers conceptual questions about quantum field theory. This includes questions on the structure of quantum gravity as a locally interacting field theory in particular.

Kolleg Mathematik Physik Berlin – KMPB

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