A bstract Perturbative scattering amplitudes in gauge theories have remarkable simplicity
and hidden infinite dimensional symmetries that are completely obscured in the …

In these introductory lectures we discuss the topic of Yangian symmetry from various
perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary …

Over the last year significant progress was made in the understanding of the computation of
Feynman integrals using differential equations (DE). These lectures give a review of these …

Outlining a revolutionary reformulation of the foundations of perturbative quantum field
theory, this book is a self-contained and authoritative analysis of the application of this new …

A bstract We compute the six-particle maximally-helicity-violating (MHV) and next-to-MHV
(NMHV) amplitudes in planar maximally supersymmetric Yang-Mills theory through seven …

The analytic structure of scattering amplitudes is restricted by Steinmann relations, which
enforce the vanishing of certain discontinuities of discontinuities. We show that these …

We establish a direct connection between scattering amplitudes in planar four-dimensional
theories and a remarkable mathematical structure known as the positive Grassmannian. The …

At the fundamental level, the interactions of elementary particles are described by quantum
gauge field theory. The quantitative implications of these interactions are captured by …

We propose a nonperturbative formulation of planar scattering amplitudes in N= 4
supersymmetric Yang-Mills theory, or, equivalently, polygonal Wilson loops. The …

A bstract We reformulate the heptagon cluster bootstrap to take advantage of the Steinmann
relations, which require certain double discontinuities of any amplitude to vanish. These …