Positive geometries provide us with a new, geometric understanding of many observables in quantum field theories. They have emerged in the study of scattering amplitudes for maximally supersymmetric Yang-Mills theory in four dimensions, in the form of the Amplituhedron. Subsequently, they have been applied to variety of models, ranging from scalar quantum field theories to string theory. Nevertheless, not many is known about positive geometries in general and many statements in physics are still conjectural. The project will focus on uncovering new structure for positive geometries and applying them to physics.
Relevant keywords for this project are:
- Kinematic Associahedron
- Cosmological Polytope
- Positive geometries in Conformal Field Theories