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For a noncommutative algebra $A$ and an antilinear automorphism $\rho$ of $A$ there is a notion of positive trace. On the physics side, positive traces are related to quantizations of superconformal field theories. On the mathematical side, positive traces are connected to spherical unitary representations of complex Lie groups. We will discuss the classification of positive traces in the case when the algebra $A$ is a deformation or a $q$-deformation of a Kleinian singularity of type A.

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The current progress in gravitational wave detection opened a new exciting window in cosmology. It is natural to ask ourselves how we can best use this new tool to explore physics beyond the standard model. With this idea in mind, my collaborators and I asked what we could learn from Cosmological Gravitational Wave Backgrounds if they were to be detected to a certain accuracy. By drawing comparison to the cosmic microwave background, we investigate the impact of elastic scattering on any cosmological background. Specifically, we focus on quantifying spectral distortions in the energy density spectrum of CGWB attributed to interaction with beyond-the-standard-model particles. We will also explore the effect that elastic scattering of graviton of Primordial Black holes would have on CGWB in the regime where PBHs account for all the dark matter.

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Zoom link https://pitp.zoom.us/j/98460268383?pwd=RytzWHd5dU1lenRhWG1NYXM3OVJpQT09