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I will connect approaches to classical integrable systems via 4d Chern-Simons theory and via symmetry reductions of the anti-self-dual Yang-Mills equations. In particular, I will consider holomorphic Chern-Simons theory on twistor space, defined using a range of meromorphic (3,0)-forms. On shell these are, in most cases, found to agree with actions for anti-self-dual Yang-Mills theory on space-time. Under symmetry reduction, these space-time actions yield actions for 2d integrable systems. On the other hand, performing the symmetry reduction directly on twistor space reduces the holomorphic Chern-Simons action to 4d Chern-Simons theory.

Zoom Link: https://pitp.zoom.us/j/99193672959?pwd=RUJ3N3h2V3RFK3ZNVVVCK1E3bXJ2Zz09

Many cosmological scenarios beyond the Standard Model lead to the formation of a network of cosmic strings. In this talk, I will review how these models lead in a natural way to the production of a stochastic gravitational wave background and how this signal could account for the recently reported results from the NANOGrav collaboration. Finally, we will explain how future observations could allow us to confirm this interpretation of the NANOGrav data.