In recent years a novel geometric picture has emerged for scattering amplitudes in planar maximally supersymmetric Yang-Mills theory. Generalizing the notion of polytopes into the Grassmannian space, the amplituhedron is a geometry encoding all the information on the physics of amplitudes at tree and loop level. In this geometric description, fundamental physical concepts like locality and unitarity are emergent and they are consequence of the geometry itself. The amplituhedron has helped to reveal an unexpected interplay between physics and geometry in other areas of theoretical physics as well. It became the first example of a vast family of the so-called positive geometries, which nowadays providea geometric description for many other physical quantities.
Some examples are the kinematic associahedron, the geometry associated to cubic scalar theory, and the cosmological polytope, which computes the wavefunction of the universe. Positive geometries make their appearance also in more general conformal field theories, beyond maximally supersymmetric Yang-Mills.
The MITP workshop will focus on understanding these new connections between physics and geometry. It will gather experts in relevant branches of physics and mathematics to advance our understanding of positive geometries and their applications to fundamental physics. The ultimate goal is to shed light on the mathematical structures of some of the most fundamental objects in theoretical physics, and to use insights from modern mathematics to develop novel and powerful tools for computing observables in quantum field theories.
