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A joint Guelph-Waterloo Gravity Group/Perimeter Institute Seminar --------------------------------------------------------------------------- Observational evidence suggests that the large scale dynamics of the universe is presently dominated by dark energy, meaning a non-luminous cosmological constituent with a negative value of the pressure to density ratio w, which would be unstable if purely fluid, but could be stable if effectively solid with sufficient rigidity. It was suggested by Bucher and Spergel that such a solid constituent might be constituted by an effectively cold (meaning approximately static) distribution of cosmic strings with w=-1/3, or membranes with the observationally favoured value w=-2/3, but it was not established whether the rigidity in such models actually would be sufficient for stabilisation. For cases (exemplified by an approximately O(3) symmetric scalar field model) in which the number of membranes meeting at a junction is even (though not if it is odd) it is easy to obtain an explicit evaluation of the rigidity to density ratio, which is shown to 3/15 in both string and membrane cases, and it is confirmed that this is indeed sufficient for stabilisation.

One of the central critical results in the theory of fault-tolerant quantum computation is that arbitrarily long reliable computation is possible provided the error rate per gate and per time step is below some threshold value. This was proved by a number of groups, but the detailed published proofs are complex and furthermore only hold for concatenation of quantum error-correcting codes able to correct 2 errors per block, while typically the best estimates of the threshold value are based on the 7-qubit code, which only corrects 1 error per block. I will describe recent work by Panos Aliferis, John Preskill, and myself which substantially simplifies existing proofs and applies as well to the concatenated 7-qubit code. The new proof also provides a nice framework in which to attempt to prove relatively high values of the threshold, which so far have only emerged as estimates from simulations

Since the seminal discovery of the neutrino by Cowan and Reines in the late 1950's, intense experimental and theoretical effort has focused on the elucidation of neutrino properties and the role they play in elementary particle physics, astrophysics, and cosmology. Neutrinos are born in the fusion reactions powering our Sun and are thought to be the driving mechanism for supernova explosions. Neutrinos exist in copious amounts as the primordial afterglow of the Big Bang and, if massive, would play a role in the evolution and ultimate fate of the Universe. Central to many of the key issues in neutrino physics is the question of whether neutrinos possess non-zero rest mass. If neutrinos are massive, then one expects flavor mixing to occur in the neutrino sector which could lead to the phenomena of neutrino oscillations and the possibility of CP violation in the neutrino sector. A detailed understanding of the microscopic properties of neutrinos can serve to pave the way to a unified description of the fundamental forces of Nature.

In this talk we assume that Quantum Einstein Gravity (QEG) is the correct theory of gravity on all length scales. We use both analytical results from nonperturbative renormalization group (RG) equations and experimental input in order to describe the special RG trajectory of QEG which is realized in Nature. We identify a regime of scales where gravitational physics is well described by classical General Relativity. Strong renormalization effects occur at both larger and smaller momentum scales. The former are related to the (conjectured) nonperturbative renormalizability of QEG. The latter lead to a growth of Newton's constant at large distances. We argue that this effect becomes visible at the scale of galaxies and could provide a solution to the astrophysical missing mass problem which does not require dark matter. A possible resolution of the cosmological constant problem is proposed by noting that all RG trajectories admitting a long classical regime automatically imply a small cosmological constant.

We propose a grand unified theory (GUT) in which the gauge symmetry is dynamically broken by a strongly coupled gauge interaction, analogous to the chiral symmetry breaking in QCD or technicolor theory. GUT is a beautiful idea and surprisingly consistent with supersymmetry (SUSY). As well as the fact that all the fermions fit to a representation in GUT groups, the three gauge coupling constants meet at a very high energy scale with the particle content of the minimal SUSY standard model. However, the realistic model building of GUT has various difficulties such as the doublet-triplet Higgs mass splitting problem and the too rapid proton decay. Also, since the GUT appears to be a theory at very high energy scale, it is the usual case that there is no definite prediction to the low energy physics. We propose a realistic model without above problems by using the dynamical GUT symmetry breaking. The model provides an interesting predictions to the gaugino mass relation in low energy which should be easily testable with the LHC and a linear collider.