Quantum Gravity

Observers agree that a citizen of Ohio had much larger voting power than a citizen of Texas or California in the recent US presidential election. Why is it so? A brief introduction to the theory of voting will be provided. We analyze the voting power of a member of a voting body, or of a person which elects his representative, who will take part in the voting on her behalf. The notion of voting power is illustrated by examples of the systems of voting in the European Council. We propose a representative voting system based on the square root law of Penrose. Using statistical approach and considering fictitious countries with randomly chosen populations we study the problem of selecting an optimal quota.

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.