We study the spectral geometric properties of the scalar Laplace-Beltrami operator associated to the Weil-Petersson metric gWP on Mγ , the Riemann moduli space of surfaces of genus γ > 1. This space has a singular compactification with respect to gWP, and this metric has crossing cusp-edge singularities along a finite collection of simple normal crossing divisors. We prove first that the scalar...

I provide a background of groups viewed as metric spaces to introduce the notion of asymptotic dimension of a group. I analyze the asymptotic dimension of Z ⊕ Z and the free group on two generators to better understand the concept of asymptotic dimension. The asymptotic dimension of the Heisenberg group, H, asdimH, has been shown to be three using advanced mathematics. I will try to show that a...

It has been observed repeatedly that the standard safety-liveness classi cation for properties of reactive systems does not t for real-time properties. This is because the implicit \liveness" of time shifts the spectrum towards the safety side. While, for example, response | that \something good" will happen eventually | is a classical liveness property, bounded response | that \something good"...

We study the slow-roll inflationary dynamics in a self-gravitating induced gravity braneworld model with bulk cosmological constant. For E ≫ M3 5 /M2 4 we find important corrections to the four-dimensional Friedmann equation which bring the standard chaotic inflationary scenario in closer agreement with recent observations. For M3 5 /M 2 P l ≪ E ≪ M3 5 /M2 4 we find five-dimensional corrections...

Buoyancy acting on plankton, i.e. the difference in specific gravity between plankton and the ambient water, is a function of salinity and temperature. From specific gravity measurements of marine fish eggs salinity appears to be the only determinant of the buoyancy indicating that the thermal expansions of the fish egg and the ambient seawater are equal. We analyze the mechanisms behind therma...

We study the black hole entropy as entanglement entropy and propose a resolution to the species puzzle. This resolution comes out naturally due to the fact that in the presence of N species the universal gravitational cutoff is Λ = MPlanck/ √ N , as opposed to MPlanck. We demonstrate consistency of our solution by showing the equality of the two entropies in explicit examples in which the relat...

We propose a novel but natural definition of conserved quantities for gravity models quadratic and higher in curvature. Based on the spatial asymptotics of curvature rather than of metric, it avoids the GR energy machinery’s more egregious problems–such as zero energy “theorems” and failure in flat backgrounds – in this fourth-derivative realm. In D > 4, the present expression indeed correctly ...

We show that the matrix-model action for noncommutative U(n) gauge theory actually describes SU(n) gauge theory coupled to gravity. This is elaborated in the 4-dimensional case. The SU(n) gauge fields as well as additional scalar fields couple to an effective metric Gab, which is determined by a dynamical Poisson structure. The emergent gravity is intimately related to noncommutativity, encodin...

We show that a canonical transformation converts, up to a boundary term, a generic 2D dilaton gravity model into a bosonic string theory with a Minkowskian target space.