Talks

The flow associated to a given smooth vector field $u(t,x)$ is well-defined, it is smooth, and it can be used to solve the classical linear PDEs associated to $u$, namely the transport and the continuity equations. The situation is substantially different when $u$ is not smooth (e.g. when $u$ is not Lipschitz continuous in the space variable, but only Sobolev or BV). Goal of the lecture is to provide an overview on classical and recent results about flow maps and PDEs associated to non-smooth vector fields.

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.

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.