Grassmannian Geometry and the Analytic S-Matrix

Who: Jacob Bourjaily (Niels Bohr Institute)
When: Monday, September 8, 2014 at 14:15
Where: The CP³ meeting room

In the past ten years, the study of scattering amplitudes in quantum field theory has led to a revolutionary reformulation of the subject. This story began in 2005 with the discovery of a recursive expansion for scattering amplitudes (to leading order) in terms of planar, trivalent, two-colored graphs (now) called “on-shell diagrams”. Around the same time that these diagrams were first drawn by physicists, they were also being drawn in the mathematical literature—for entirely independent reasons—in the context of what is known as the “positroid stratification” of the Grassmannian of k-planes in n-dimensions. These two communities recently came into contact, and the correspondence has led to many valuable insights on both sides. In my talk, I will outline the physical ideas behind these developments, and explain the many deep connections which have been found between scattering amplitudes and the geometry and combinatorics of the positroid stratification of the Grassmannian.