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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

In this talk, I will begin with a brief introduction to celestial holography and setting up the celestial amplitudes, before diving into some recent results on examining the BCFW recursion relations for celestial amplitudes. We start by recasting the celestial incarnation of the BCFW shift as a generalization of the action of familiar asymptotic symmetries on hard particles, before focusing on two limits: large-z and infinitesimal-z. We then discuss how the celestial CFT data encodes the large-z behavior determining which shifts are allowed, while the infinitesimal limit is tied to the celestial bootstrap program via the BG equations that constrain the MHV sector.

Zoom link: https://pitp.zoom.us/j/99231185135?pwd=OWk4S2ZITmFGSmVsQUwwbHI5NW1rUT09

The search for pragmatic observables of quantum gravity remains at the forefront of fundamental physics research. A large set of ideas collectively known as the gauge-gravity duality have proven fruitful in tackling this problem. While such a duality is believed to universally govern gravitational theories, its nature in theories of gravity that describe our universe to a good degree of approximation is still little understood.

In this talk I will discuss efforts in formulating a holographic correspondence for gravity in four-dimensional asymptotically flat spacetimes. The proposed dual theory lives on a two-dimensional celestial sphere at infinity and is constrained by a wide range of symmetries. I present recent evidence for this proposal by showing that it arises naturally in a flat space limit of AdS/CFT. I will illustrate this construction with two related examples: the propagation of a particle in a shockwave background and the high-energy scattering of 2 particles.

Zoom Link: https://pitp.zoom.us/j/97426266597?pwd=UmhncFR6NExFVzI2SlJwdE1LeUlIQT09