A positive path from Teichmüller spaces to scattering amplitudes

It was recently appreciated how scattering amplitudes in a large class of theories can be described as a "curve integral", i.e. as an integral over the space of curves that can be drawn on a Riemann surface. At the heart of this formalism is a new description of Teichmuller space - and generalizations thereof - by polynomial equations to be solved over positive variables.

In this talk I will review these progresses, walking a path from purely combinatorial considerations about curves on surfaces, through tropical formulae for particle scattering amplitudes, and culminating in the positive description of Teichmuller space.

This talk is based on 2309.15913 and 2311.09284.