Search Talks

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. In network geometry a crucial problem is the identifications of mechanisms to describe emergent network geometry. In this talk, after an introduction to complex network theory, l will present a class of non–equilibrium models [1-4] in which geometrical properties of the networks emerge spontaneously from their dynamics. Specifically we will discuss the model called network geometry with flavor (NGF).The NGF can generate discrete geometries of different nature, ranging from chains and higher dimensional manifolds to scale-free complex networks. Interestingly the NGF with fitness of the nodes reveals relevant relations with quantum statistics. In fact the faces of the NGF have generalized degrees that follow either the Fermi-Dirac, Boltzmann or Bose-Einstein statistics depending on their flavor and on their dimensionality. Specifically, NGFs with flavor s=-1, when constructed in dimension d=3 gluing tetrahedra along their triangular faces, have the generalized degrees of the triangular faces, of the links, and of the nodes following respectively the Fermi-Dirac, the Boltzmann or the Bose-Einstein distribution. 

[1] G. Bianconi, Interdisciplinary and physics challenges in network theory, EPL 111, 56001 (2015).
[2] Z. Wu, G. Menichetti C. Rahmede G. Bianconi, Emergent Complex Network Geometry, Scientific Reports 5, 10073 (2015).
[3] G. Bianconi and C. Rahmede, Complex Quantum Network Manifolds are Scale-Free in d>2, Scientific Reports 5, 13979 (2015)
[4] G. Bianconi and C. Rahmede, Network geometry with flavor: from complexity to quantum geometry, arxiv:1511.04539 (2015)

LIGO's first observing run which ended in January 2016 yielded two unambiguous gravitational wave signals (GW150914 and GW151226) from the merger of binary black holes as well as a possible third signal (LVT151012). I will review our current estimates of the parameters of the source systems as well as possible formation scenarios. I will discuss how joint analyses of GW150914 and GW151226 allow us to place bounds on departures from general relativity, infer astrophysical binary black hole formation rates, and constrain the mass distribution of coalescing black hole systems. Additionally, I will review the status of searches for other types of gravitational wave signals in data from LIGO's first observing run as well as the implications of the nondetection of gravitational waves from the merger of binary neutron star and neutron-star-black-hole systems. Finally, with the start of LIGO's second observing run within the next few weeks, I will outline our expectations for new detections and scientific prospects.

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.