Talks

Although the inflationary predictions for the primordial power spectrum of    density inhomogeneities   seem  very successful, there is an obscure part in our understanding of the emergence of the seeds of cosmic   structure:  How  does  a universe which at one pint  in time is described by a  state that is fully  homogeneous and isotropic,  evolve into a state that is not,   given that the dynamics  does not  contain any  source  for the  undoing of  such symmetry?   We will  discuss  an   approach that  offers  a resolution  of the  issue  in the context of  proposals to deal  with the measurement  problem in quantum  mechanics. We will  see that the   approach  naturally  resolves the difficulties  raised  by the  lack of  observation of tensor modes.

Path integrals are at the heart of quantum field theory. In spite of their covariance and seeming simplicity, they are hard to define and evaluate. In contrast, functional differentiation, as it is used, for example, in variational problems, is relatively straightforward. This has motivated the development of new techniques that allow one to express functional integration in terms of functional differentiation. In fact, the new techniques allow one to express integrals in general through differentiation. These techniques therefore add to the general toolbox for integration and integral transforms such as the Fourier and Laplace transforms. Here, we review some of these results, we give simpler proofs and we add new results, for example, on expressing the Laplace transform and its inverse in terms of derivatives, results that may be of use in quantum field theory, e.g., in the context of heat traces.

Similarly to the probability distribution of energy in physics, the probability distribution of money among the agents in a closed economic system is also expected to follow the exponential Boltzmann-Gibbs law, as a consequence of entropy maximization.  Analysis of empirical data shows that income distributions in the USA, European Union, and other countries exhibit a well-defined two-class structure.  The majority of the population (about 97%) belongs to the lower class characterized by the exponential ("thermal") distribution.  The upper class (about 3% of the population) is characterized by the Pareto power-law ("superthermal") distribution, and its share of the total income expands and contracts dramatically during booms and busts in financial markets.  Globally, data analysis of energy consumption per capita around the world shows decreasing inequality in the last 30 years and convergence toward the exponential probability distribution, in agreement with the maximal entropy principle. Similar results are found for the global probability distribution of CO2 emissions per capita.  All papers are available at http://physics.umd.edu/~yakovenk/econophysics/.  For recent coverage in Science magazine, see http://www.sciencemag.org/content/344/6186/828

In order to introduce the cosmological constant in a simplicial geometry, constant curvature should be introduced on simplex faces. This yields a compactification of the phase space and the finiteness of the Hilbert for each link. Not only the intrinsic, but also the extrinsic geometry turns out to be discrete, pointing to discreetness of time, in addition to space.

Quantum effects render black holes unstable.  Besides Hawking radiation there is another, genuinely quantum gravitational, source of instability: the Hajicek-Kiefer explosion via tunnelling to a white hole.  A recent result in classical general relativity makes this decay channel plausible: there is an exact external solution of the Einstein equations locally (but not globally) isometric to extended Schwarzschild, which describes an object collapsing into a black hole and then exploding out of a white hole. The tunnelling time can in principle be computed using Loop Quantum Gravity. If it is sufficiently short, present explosions of primordial black hole could be observables, opening a new observational window on quantum gravity. I discuss the possibility that these explosions could be related to the recently observed and mysterious Fast Radio Bursts. 

Niels Bohr was Nobel-winning physicist – a pioneer of quantum theory – but his influence extended far beyond his own research. He was a gifted teacher who established one of the 20th century’s most important centres for physics, and was instrumental in the development of physics worldwide. He became a statesman following the Second World War, calling for international cooperation to avoid nuclear conflict. Bohr’s legacy – in science, humanitarianism, and family – spans generations, as his grandson will illustrate during a special public lecture webcast at Perimeter Institute. Dr. Vilhelm Bohr, a researcher at the National Institute on Aging in Maryland and Chairman of the Niels Bohr Archive in Copenhagen, will provide unique insights into his grandfather’s multifaceted personality, as well as the important influence of Niels Bohr’s father, wife, and brother.

I will present a novel approach to explain the smoothness and flatness of the universe on large scales and the generation of a nearly scale-invariant spectrum of adiabatic density perturbations.