Holography, Amplitudes and the Swampland
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The Swampland program aims to understand constraints on effective theories which arise through the requirement of the existence of an ultraviolet completion to quantum gravity. To date, research has primarily utilized evidence from string theory examples to propose and test such constraints. In this talk, I will discuss the potential for progress by using other approaches, specifically, properties of scattering amplitudes and of Conformal Field Theories (through holography). I will illustrate such connections through recent work which connects the Weak Gravity Conjecture on the one hand to certain convexity properties of charged operators in CFTs, and on the other hand to growth of scattering amplitudes of massive spin-2 particles in the Regge regime.