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The 6d N = (2,0) theories are superconformal field theories believed to describe the low-energy dynamics of N coincident M5-branes. These theories don't have a known lagrangian description and remain largely mysterious, so it is an interesting question how one might calculate observables there.  An exciting prospect is to use the analytical conformal bootstrap, which offers a way to systematically calculate 1/N corrections at large N. In this talk I will present the bootstrap approach to a case study, that of calculating the 2-point function of stress tensors in the presence of a surface defect.  This setup turns out to be remarkably simple and helps us address some technical issues faced in similar calculations, notably we can derive a supersymmetric inversion formula and check crossing symmetry explicitly. I will also comment on the interpretation of our result in the context of holography, of the chiral algebra construction of Beem et al. and on what it can reveal about the interactions between M2 and M5-branes.

Zoom link:  https://pitp.zoom.us/j/92631930165?pwd=Qm9MQzlNdHo0WGJINUZBUVNaOXZxZz09

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