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Area metrics define generalized geometric backgrounds to describe spacetime. They are suggested at various places in classical field theory and arise within different approaches to quantum gravity. On these grounds, after introducing the notion of an area metric, I will consider covariant area-metric actions to second order in fluctuations and derivatives. I will then show how these give rise to effective length-metric actions with a distinct nonlocal Weyl-curvature squared term beyond general relativity. Finally, I will point out possible implications and routes for phenomenology.

Covariant loop quantum gravity, commonly referred to as the spinfoam model, provides a regularization for the path integral formalism of quantum gravity. A 4-dimensional Lorentzian spinfoam model with a non-zero cosmological constant has been developed based on quantum SL(2,C) Chern-Simons theory on a graph-complement three-manifold, combined with loop quantum gravity techniques. In this talk, I will give an overview of this spinfoam model and highlight its inviting properties, namely (1) that it yields finite spinfoam amplitude for any spinfoam graph, (2) that it is consistent with general relativity with a non-zero cosmological constant at its classical regime and (3) that there exists a concrete, feasible and computable framework to calculate physical quantities and quantum corrections through stationary phase analysis. I will also discuss recent advancements in this spinfoam model and explore its potential applications.

In this talk I will discuss the potential of future high-resolution CMB observations to probe structure on sub-galactic scales. In particular, I will discuss how a CMB-HD experiment can measure lensing over the range 0.005 h/Mpc < k < 55 h/Mpc, spanning four orders of magnitude, with a total lensing signal-to-noise ratio from the temperature, polarization, and lensing power spectra greater than 1900. These lensing measurements would allow CMB-HD to distinguish between cold dark matter (CDM) and non-CDM models that can resolve apparent small-scale tensions with CDM. In addition, CMB-HD can distinguish between baryonic feedback effects and non-CDM models due to the different way each impacts the lensing signal. The kinetic Sunyaev-Zel’dovich power spectrum measured by CMB-HD further constrains non-CDM models that deviate from CDM. In sum, future CMB experiments will not only measure traditional cosmological parameters with unprecedented precision, but will also simultaneously constrain baryonic physics and dark matter properties that impact sub-galactic scales.

Hawking’s seminal result, that black holes behave as black bodies with a non-vanishing temperature, suggests that black holes should evaporate. However, Hawking’s derivation is incomplete, as it neglects the backreaction between radiation and geometry. In this talk, we will present a novel approach to black hole perturbation theory that incorporates backreaction and is valid to arbitrary order. The applications to the physics of evaporating black holes is discussed, and we explore potential experimental implications. The intention is to eventually derive corrections to semi-classical computations in the literature and to determine the fate of evaporating black holes.

The underlying holomorphic structure of a generalized Kahler manifold has been recently understood to be a square in the double category of holomorphic symplectic groupoids (or (1,1)-shifted symplectic stacks). I will explain what this means and how it allows us to describe the generalized Kahler metric in terms of a single real scalar function, resolving a conjecture made by physicists Gates, Hull, and Rocek in 1984. This is based on joint work with Yucong Jiang and Daniel Alvarez available at https://arxiv.org/abs/2407.00831.