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There exists a solid framework to study gravitational waves in full, non-linear general relativity when the spacetime is asymptotically flat. An essential aspect of this framework is asymptotic symmetries. These symmetries are the BMS symmetries. The situation for cosmological spacetimes is different, however. Expanding spacetimes, whose expansion is decelerating such as matter- or radiation-dominated universes, share some similarities with the asymptotically flat case nonetheless. Not surprisingly, their asymptotic symmetries also share similarities with the BMS symmetries, but are not the same.

Zoom Link:  https://pitp.zoom.us/j/98168915236?pwd=ejFtaVpVZXAxT2NIdDhtMUNSbmRvQT09

We present a new class of supersymmetric localization principles in the context of supersymmetric quantum mechanics. Contrary to the standard localization, this new principle deals with non-supersymmetric observables. We apply this to provide a path integral understanding of trace formulas in mathematics. Our examples will contain both integrable and chaotic quantum systems, namely trace formulas on compact Lie groups by Eskin, and generic locally symmetric space by Selberg. 

Zoom Link:  https://pitp.zoom.us/j/99332291865?pwd=c0kyUUlWN1AxeXpvNmRkNHRSRXNXdz09

I will argue that many theories in which dark matter is light (with a mass < eV) lead to theoretically and observationally interesting dark matter substructure. As a particular, calculable, example I will show that this is the case for a new vector boson with non-zero mass (a `dark photon') that is present during inflation, at which time a relic abundance is automatically produced from vacuum fluctuations.  Due to a remarkable coincidence between the size of the primordial density perturbations and the scale at which quantum pressure is relevant, a substantial fraction of the dark matter inevitably collapses into gravitationally bound solitons, which are fully quantum coherent objects. The central densities of these `dark photon star', or `Proca star', solitons are typically a factor 10^6 larger than the local background dark matter density today. I will also mention how similar substructure might occur in theories of post-inflationary axion-like-particles. 

Zoom Link:  https://pitp.zoom.us/j/94995778057?pwd=T2w4WWU0ZGtwWEIzTHFSZ3J6dGovUT09