Talks

We construct the phase space of a spherically symmetric causal diamond in (d+2)-dimensional Minkowski spacetime. Utilizing the covariant phase space formalism, we identify the relevant degrees of freedom that localize to the d-dimensional bifurcate horizon and, upon canonical quantization, determine their commutators. On this phase space, we find two Iyer-Wald charges. The first of these charges, proportional to the area of the causal diamond, is responsible for shifting the null time along the horizon and has been well-documented in the literature. The second charge is much less understood, being integrable for d ≥ 2 only if we allow for field-dependent diffeomorphisms and is responsible for changing the size of the causal diamond. 

Big Bang Nucleosynthesis (BBN) is a powerful tool for probing both new physics and LCDM, and complements analyses utilizing the Cosmic Microwave Background (CMB) and results from particle experiment.  I will provide two examples of BBN probes of BSM models.  I will then discuss new kinds of analyses that can be performed with the recently-released fast and differentiable BBN code LINX.  In particular, LINX can be used to perform full BBN+CMB joint analyses at a level of sophistication that has never been achieved before, even in LCDM analyses.

Recent advances in General Relativity point toward unanticipated, and dynamic, relations between ultracompact objects and the universe they inhabit. The possibility for strongly gravitating systems, like astrophysical black holes (BHs) and their embedding cosmology, to directly interact has been dubbed "cosmological coupling." We focus on recent results from the DOE Stage IV Dark Energy (DE) Spectroscopic Instrument (DESI), which strongly suggest that DE is dynamical. Using typical empirical models for the cosmic star-formation rate density as a proxy to BH production, we show that the DESI-inferred time-evolution of DE is consistent with cosmologically coupled stellar-collapse BHs as the source of DE. The predicted cosmological expansion rate today, H_0 = 69.94 +/- 0.81 km/Mpc/s, is in excellent agreement with H_0 = 69.58 +/- 1.58 km/Mpc/s recently reported by the Chicago-Carnegie Hubble Program using Cepheid, Tip of the Red Giant Branch, and J-Region Asymptotic Giant Branch stellar distance-ladder calibrations. With DESI Redshift Space Distortions and Year 3 datasets on the horizon, we highlight exciting prospects for further observational confrontation in the near term.

In this lecture I will explain a second type of iteration, introduced by La'szlo' and myself, which produces continuous solutions of incompressible Euler in a fashion which shares a lot of similarities with the theorem of Nash explained in Lecture 3.

In the recent resolution of the strong Onsager’s conjecture in L^3 framework, so-called wavelet-inspired Nash’s iteration has been developed. In this lecture, we will sketch this new method and provide the necessary background. The lecture will be based on our recent joint work with Matthew Novack.