FEYNMAN AMPLITUDES, PERIODS AND MOTIVES. VOLUME: 648

This volume contains the proceedings of the International Research Workshop on Periods and Motives--A Modern Perspective on Renormalization, held from July 2-6, 2012, at the Instituto de Ciencias Matemáticas, Madrid, Spain.

Feynman amplitudes are integrals attached to Feynman diagrams by means of Feynman rules. They form a central part of perturbative quantum field theory, where they appear as coefficients of power series expansions of probability amplitudes for physical processes. The efficient computation of Feynman amplitudes is pivotal for theoretical predictions in particle physics.

Periods are numbers computed as integrals of algebraic differential forms over topological cycles on algebraic varieties. The term originated from the period of a periodic elliptic function, which can be computed as an elliptic integral.

Motives emerged from Grothendieck's "universal cohomology theory", where they describe an intermediate step between algebraic varieties and their linear invariants (cohomology). The theory of motives provides a conceptual framework for the study of periods. In recent work, a beautiful relation between Feynman amplitudes, motives and periods has emerged.

The articles provide an exciting panoramic view on recent developments in this fascinating and fruitful interaction between pure mathematics and modern theoretical physics.

Readership
Graduate students and research mathematicians interested in modern theoretical physics and algebraic geometry.

Authors
Luis Álvarez-Cónsul, José Ignacio Burgos-Gil, and Kurusch Ebrahimi-Fard, Instituto de Ciencias Matemáticas, Madrid, Spain

Table of Contents
S. Bloch -- A note on twistor integrals
C. Bogner and M. Lüders -- Multiple polylogarithms and linearly reducible Feynman graphs
P. Brosnan and R. Joshua -- Comparison of motivic and simplicial operations in mod-l-motivic and étale cohomology
S. Carr, H. Gangl, and L. Schneps -- On the Broadhurst-Kreimer generating series for multiple zeta values
C. Delaney and M. Marcolli -- Dyson-Schwinger equations in the theory of computation
C. Duhr -- Scattering amplitudes, Feynman integrals and multiple polylogarithms
V. Golyshev and M. Vlasenko -- Equations D3 and spectral elliptic curves
D. Kreimer -- Quantum fields, periods and algebraic geometry
E. Panzer -- Renormalization, Hopf algebras and Mellin transforms
I. Soudères -- Multiple zeta value cycles in low weight
S. Weinzierl -- Periods and Hodge structures in perturbative quantum field theory
K. Yeats -- Some combinatorial interpretations in perturbative quantum field theory