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Recent observations of gravitational waves represent a remarkable success of our theoretical models of relativistic binaries. However, accurate models are largely restricted to binaries in which the two members have roughly equal masses; for binaries with more disparate masses, modelling is less mature. This is especially relevant for extreme-mass-ratio inspirals (EMRIs), in which a stellar-mass object orbits a supermassive black hole in a galactic core. EMRIs are uniquely precise probes of black hole spacetimes, and they will be key targets for the space-based detector LISA. They are best modelled by gravitational self-force theory, in which the smaller object generates a small gravitational perturbation that reacts back on it to exert a "self-force", accelerating the object away from geodesic motion. For LISA science, we must work to second order in this perturbative treatment. In this talk, I discuss the foundations of self-force theory, its application to EMRIs, and the current status of first- and second-order models.

Our ability to model cosmological observations has reached an awesome level, a tour de force of observational innovation, sophisticated statistical inference, and delicate numerical computation. There’s little doubt that the Standard Cosmological Model will stand the test of time. But what has it told us and what is still missing? What are the prospects for learning particle physics and condensed matter from cosmology? And what can the path we’ve taken to reach this point tell us about where it might lead?

The elliptic genus is a powerful deformation invariant of 1+1D SQFTs: if it is nonzero, then it protects the SQFT from admitting a deformation to one with spontaneous supersymmetry breaking. I will describe a "secondary" invariant, defined in terms of mock modularity, that goes beyond the elliptic genus, protecting SQFTs with vanishing elliptic genus. The existence of this invariant supports the hypothesis that the space of minimally supersymmetric 1+1D SQFTs provides a geometric model for universal elliptic cohomology. Based on joint works with D. Gaiotto and E. Witten.