This series covers all areas of research at Perimeter Institute, as well as those outside of PI's scope.
I will tell how the story given in Umberto Eco's book The Search for the Perfect Language continues with modern work on logical and programming languages.(For more information, see http://www.umcs.maine.edu/~chaitin/hu.html.)
Gamma-ray bursts (GRBs) -- rare flashes of ~ MeV gamma-rays lasting from a fraction of a second to hundreds of seconds -- have long been among the most enigmatic of astrophysical transients. Observations during the past decade have led to a revolution in our understanding of these events, associating them with the birth of neutron stars and/ or black holes during either the collapse of a massive star or the merger of two compact objects (e.g., a neutron star and a black hole).
The Standard model of Cosmology consists of a package of ideas that include Cold Dark Matter, Inflation, and the existence of a small Cosmological Constant. While there is no consensus about what lies beyond the Standard Model, there is a leading candidate that also includes a small package of ideas: A Landscape of connected vacua: the idea that the universe started out with a large energy density, and Coleman DeLuccia Tunneling between vacua. An additional idea that comes from string theory and black hole physics is the Holographic Principle.
The transformation of a narrow beam into a hollow cone when incident along the optic axis of a biaxial crystal, predicted by Hamilton in 1832, created a sensation when observed by Lloyd soon afterwards. It was the first application of his concept of phase space, and the prototype of the conical intersections and fermionic sign changes that now pervade physics and chemistry.
Cosmologists are struggling to understand why the expansion rate of our universe is now accelerating. There are two sets of explanations for this remarkable observation: dark energy fills space or general relativity fails on cosmological scales. If dark energy is the solution to the cosmic acceleration problem, then the logarithmic growth rate of structure $dlnG/dlna = \Omega^\gamma$, where $\Omega$ is the matter density independent of scale in a dark matter plus dark energy model.
Key notions from statistical physics, such as "phase transitions" and "critical phenomena", are providing important insights in fields ranging from computer science to probability theory to epidemiology. Underlying many of the advances is the study of phase transitions on models of networks. Starting from the classic ideas of Erdos and Renyi, recent attempts to control and manipulate the nature of the phase transition in network connectivity will be discussed.
Yes, that's indeed where it happens. These pictures are not ordinary pictures but come with category-theoretic algebraic semantics, support automated reasoning and design of protocols, and match perfectly the developments in important areas of mathematics such as representation theory, proof theory, TQFT & GR, knot theory etc. More concretely, we report on the progress in a research program that aims to capture logical structures within quantum phenomena and quantum informatic tasks in purely diagrammatic terms.
Integrability in gauge/string dualities will be reviewed in a broad perspective with a particular emphasis on the recently proposed equations describing the full planar spectrum of anomalous dimensions in AdS/CFT [N.Gromov, V.Kazakov, PV].
Physicists are often so awestruck by the lofty achievements of the past, we end up thinking all the big stuff is done, which blinds us to the revolutions ahead. We are still firmly in the throes of the quantum revolution that began a hundred years ago. Quantum gravity, quantum computers, qu-bits and quantum phase transitions, are manifestations of this ongoing revolution. Nowhere is this more so, than in the evolution of our understanding of the collective properties of quantum matter.