This series consists of talks in the area of Quantum Gravity.
A formulation of a limit of a sequence of finite non-commutative spectral triples is presented. Examples of the commutative limits are the coadjoint orbits of semisimple Lie groups.
I will give a broad overview of this old subject which has come back to light recently in connection with the issue of black hole evaporation. It will be an informal, black board talk.
The possibility of observing quantum gravitational phenomena, viewed as remote until not long ago, is increasingly considered to be plausible. A potentially observable phenomenon is the decay of black holes via a quantum gravitational tunneling akin to standard nuclear decay. Loop quantum gravity can be used to compute the corresponding lifetime. This could be much shorter than the Hawking radiation time, rendering the effect astrophysically relevant.
We introduce the construction of a new framework for probing discrete emergent geometry and boundary-boundary observables based on a fundamentally a-dimensional underlying network structure.
General relativity is invariant under diffeomorphisms, and
excitations of the metric corresponding to diffeomorphisms
are nonphysical. In the presence of a boundary, though --
including a boundary at infinity -- the Einstein-Hilbert
action with suitable boundary terms is no longer fully
invariant, and certain diffeomorphisms are promoted to
physical degrees of freedom. After briefly describing how
this happens in (2+1)-dimensional AdS gravity, I will
report on work in progress on the asymptotically flat case,
We present results from a study of Euclidean dynamical triangulations in an attempt to make contact with Weinberg's asymptotic safety scenario. We find that a fine-tuning is necessary in order to recover semiclassical behavior, and that once this tuning is performed, our simulations provide evidence in support of the asymptotic safety scenario for gravity. We discuss our motivation for the tuning and present our numerical results. Finally, we discuss what our simulations imply for the dimension of the ultraviolet critical surface, which sets the number of free parameters in the theory.
In the geometric models of matter, proposed in a joint paper with Michael Atiyah and Nick Manton, static particles like the electron or proton are modelled by Riemannian 4-manifolds. In this talk I will explain how the spin degrees of freedom appear in the geometric framework. I will also discuss a proposal for time evolution in one particular model, namely the Taub-NUT model of the electron.