Positivity with gravitons and all of that

Dispersive relations for scattering amplitudes appeared to be a useful tool in constraining effective field theories from the requirement that they have a UV completion. However, this approach is problematic in theories with the exchange of massless particles because it deals with a forward limit for scattering amplitudes. In this talk, I will formalize the application of positivity bounds for models with gravitons and show their constraining power for several models.