In this talk I will discuss how to write down generalized group-theoretic crossing equations for a unitary Euclidean CFT and how to construct an exact solution to it. I will also present its connection to the cosmological bootstrap program.

Analytic methods for studying gravitational processes have received review interest due to their application to gravitational wave phenomenology. In this direction, one of the challenges is to develop a systematic apparatus to obtain the dynamics of spinning objects from the classical limit of quantum scattering amplitudes.

Exploring the Kerr-Schild gauge properties seems promising, and...

We will discuss two classes of line defects in the O(N) critical model at the Wilson-Fisher fixed point. These extended excitations are relevant for condensed matter systems, such as doped quantum antiferromagnets. After reviewing some state-of-the-art analytic bootstrap techniques, we will apply them to compute the correlator of two bulk excitations at first order in the epsilon expansion....