Abstract:
Several recent developments in perturbative scattering amplitudes have come from studying spaces like polytopes and Grassmannians, that can be given positive real coordinates. This talk will introduce a simple, positive real way to define ''Teichmüller spaces'', which are moduli spaces of surfaces/worldsheets. This leads to a new family of formulas for string amplitudes and (non-SUSY) gauge theory amplitudes. The formulas manifest physical properties of amplitudes and also expose asymptotic behaviour in the limit of large numbers of particles, where the formulas become integrals over random walks! I will also remark on the interesting connections of this work to matrix models and integrability.