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Functions and numbers in quantum field theory

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We review recent results in the theory of functions and numbers in \phi4 theory. We will give an introduction to the following topics: graphical functions—- conformal quantum field theory functions on the complex plane, generalized single-valued hyperlogarithms—- generalizations of hyperlogarithms which are ubiquitous in graphical functions, \phi4 periods—- renormalization scheme independent contributions to the \phi4 beta function, and the Galois coaction which gives important information on the structure of \phi4 periods.

This talk is part of the Quantum Fields and Strings Seminars series.

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