Over the last decade, there has been remarkable progress in our description of particle interactions, through a deeper understanding of the hidden symmetries and geometric structures underlying scattering amplitudes - the quantities which predict the quantum interactions of particles. New and unexpected properties of remarkable mathematical beauty have been uncovered, some of them from a purely geometrical perspective with no reference to space and time.

This conference will bring together researchers working in perturbative gauge theory and gravity, as well as in mathematics, with the goals of:

• reviewing recent progress and current status,
• identifying and strengthening connections between areas of mathematics and theoretical physics relevant to quantum scattering, and
• inspiring further outstanding developments and collaborations among the participants.

Topics will include developments from the physics side such as generalized unitarity, twistor variables and topological string theory, scattering equations, recursion relations, integrability methods and the OPE, color-kinematics duality, the double-copy properties of supergravity theories and their applications to higher-spin theories and to questions relevant to cosmology as well as from the mathematics side such as the (totally non-negative) Grassmannian and polytopes, (motivic) multiple zeta values, single-valued multiple (harmonic) polylogarithms, the symbol of iterated integrals and the Amplituhedron.