Theoretical Physics Seminar: Marko Berghoff

Title: The geometry of scattering amplitudes

Abstract: Scattering amplitudes can be studied from many viewpoints, connecting them with (a priori) very different areas of mathematics. One example is the work of Bloch, Brown, Esnault, Kreimer (and others) who uncovered the (algebraic) geometry behind Feynman periods. Generalizing this approach to Feynman amplitudes poses some serious difficulties, as then the geometry depends on parameters (kinematics): Instead of single periods, we now need to understand families of periods, or rather the respective geometries. While the complete answer remains a mystery, a lot of information can already be gained from studying where and how the geometry degenerates. This "singularity theory" approach allows to determine the poles and branch points of amplitudes (the Landau variety) and make some qualitative statements about their nature. In particular, it produces vanishing criteria for iterated variations (eg (extended) Steinmann relations). This is joint work with Erik Panzer (U Oxford).