This series consists of talks in the area of Quantum Gravity.
Abstract: Complex networks describe interacting systems ranging from the brain to the Internet. While so far the geometrical nature of complex networks has been mostly neglected, the novel field of network geometry is crucial for gaining a deeper theoretical understanding of the architecture of complexity. At the same time, network geometry is at the heart of quantum gravity, since many approaches to quantum gravity assume that space-time is discrete and network-like at the quantum level.
The study of isolated systems has been vastly successful in the context of vanishing cosmological constant, $\Lambda = 0$. However, there is no physically useful notion of asymptotics for the universe we inhabit with $\Lambda > 0$. The full non-linear framework is still under development, but some interesting results at the linearized level have been obtained. I will focus on the conceptual subtleties that arise at the linearized level and discuss the quadrupole formula for gravitational radiation.
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.