Hal Haggard

Brief introduction to gravitational wave detection 

Black hole entropy is a robust prediction of quantum gravity with no observational test to date. We use the Bekenstein-Hawking entropy formula to determine the probability distribution of the spin of black holes at equilibrium in the microcanonical ensemble. We argue that this ensemble is relevant for black holes formed in the early universe and predicts the existence of a population of black holes with zero spin.

Quantum effects render black holes unstable. In addition to Hawking radiation, which leads to the prediction of a long lifetime, there is the possibility of quantum tunneling of the black hole geometry itself. A robust possibility for treating the quantum tunneling of a spacetime geometry is through a complex path integral and Picard-Lefschetz theory.

An exciting frontier in physics is to understand the quantum nature of gravitation in finite regions of spacetime. Study of these regions from ``below'', that is, by studying the quantum geometry of finite regions emerging from loop gravity and spin networks has recently resulted in a new road to the quantization of volume and to evidence that there is a robust gap in the volume spectrum. In this talk I will complement these results with recent work on conformal field theories in a particular finite region, a spherical ball of space.

The space of convex polyhedra can be given a dynamical structure. Exploiting this dynamics we have performed a Bohr-Sommerfeld quantization of the volume of a tetrahedral grain of space, which is in excellent agreement with loop gravity. Here we present investigations of the volume of a 5-faced convex polyhedron. We give for the first time a constructive method for finding these polyhedra given their face areas and normals to the faces and find an explicit formula for the volume. This results