Talks

We will discuss techniques for computing 4-point functions of local operators in 2D conformal field theories, and their implications for semiclassical 3D quantum gravity. For generic 4-point functions, we present new closed-form expansions of the Virasoro conformal blocks. Specializing to correlators of holomorphic operators, these can be efficiently and exactly determined using an analytic implementation of the conformal bootstrap. Applying this method to the sewing construction of 2D CFT partition functions, we compute, via AdS/CFT, the semiclassical expansion of pure 3D quantum gravity around saddle point geometries of genus two; unlike at genus one, this expansion does not truncate at finite loop order.  

More than a decade after its discovery, cosmic acceleration still 
poses a puzzle for modern cosmology and a plethora of models of dark energy 
or modified gravity, able to reproduce the observed expansion history, have 
been proposed as alternatives to the cosmological standard model. In recent 
years it has become increasingly evident that probes of the expansion his- 
tory are not sufficient to distinguish among the candidate models, and that 
it is necessary to combine those with observations that probe the dynamics 
of inhomogeneities. Future cosmological surveys will map the evolution of 
inhomogeneities to high accuracy, allowing us to test the relationships be- 
tween matter overdensities, local curvature, and the Newtonian potential on 
cosmological scales.

I will discuss theoretical issues involved in finding an optimal framework to 
study deviations from General Relativity on cosmological scales, giving an 
overview of recent progress, with a focus on model-independent, parametrized 
approaches. I will summarize where we stand and what are the next steps 
we should take.

The presence of an instability in the Standard Model Higgs potential may have important implications for inflation and the viability of our Universe. In particular, if the Hubble scale during inflation is comparable to (or larger than) the instability scale of the potential, quantum fluctuations in the Higgs field will lead to the Higgs sampling the unstable part of the potential during inflation. However, to correctly study transitions to the unstable regime and determine the significance for the resulting universe requires addressing a number of subtleties. I will discuss these subtleties and a variety of possible approaches to studying Higgs evolution during inflation. By considering both (1) the evolution of Higgs fluctuations in the Gaussian approximation and (2) a perturbative calculation of the fluctuation two-point correlation function, I aim to elucidate how to address these issues in a consistent, physical way. The insight provided by these approaches will set the scene for studying Higgs fluctuations via the Fokker-Planck (FP) approach, which captures the non-Gaussian nature of the field. As such, it provides information about the rare—but, in terms of the fate of our Universe, potentially extremely important—patches that experience particularly large fluctuations.