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I will explain a new 2d gravity/matrix model duality. The bulk theory can be defined as a minimal string theory whose matter sector is given by timelike Liouville theory instead of a minimal model. The theory admits a dual description in terms of a double-scaled matrix integral whose leading density of states is given by the universal Cardy density of states in a 2d CFT of central charge c, thus motivating us to call the bulk theory the Virasoro minimal string. The duality can be derived by exploiting a certain relation to 3d gravity compactified on a circle. For large central charge, it reduces to the duality between JT-gravity and the corresponding double-scaled matrix integral. Based on work in collaboration with Scott Collier, Beatrix Mühlmann and Victor Rodriguez.

Richard Feynman's last blackboard at Caltech contains a number of tantalizing inscriptions about Bethe Ansatz in quantum integrable models, which fascinated him in the last years of his life. After reviewing some basic examples, I will present a modern perspective on the subject, linking it to dualities in QFT and String Theory, as well as the Langlands duality in mathematics. I will then discuss some recent developments that lend support to Feynman's intuition that these ideas could be useful in the study of 4d gauge theory, and formulate some open questions.

What can be measured asymptotically in quantum field theory? Among the answers to this question are scattering amplitudes, but also a whole compendium of inclusive measurements, such as expectation values of gravitational radiation and out-of-time-ordered amplitudes. We show that these asymptotic observables can be related to one another through new versions of crossing symmetry. Assuming analyticity, we propose generalized crossing relations and corresponding paths of analytic continuation. Throughout the talk, we show how to apply crossing in practice, using various tree- and loop-level examples.