The open string on the plane-wave limit of dSn × Sn with constant B2 and dilaton background fields is canonically quantized. This entails solving the classical equations of motion for the string, computing the symplectic form, and defining from its inverse the canonical commutation relations. Canonical quantization is proved to be perfectly suited for this task, since the symplectic form is una...

Einstein's general relativity can emerge from pregeometry, with the metric composed of more fundamental fields. We formulate euclidean pregeometry as a SO(4) - Yang-Mills theory. In addition to gauge fields we include vector field in representation group. The and diffeomorphism invariant kinetic terms for these permit well-defined functional integral, contrast gravity Einstein-Hilbert action. p...

We consider the geometric non-linear inverse problem of recovering a Hermitian connection $A$ from source-to-solution map cubic wave equation $\\Box{A}\\phi+\\kappa |\\phi|^{2}\\phi=f$, where $\\kappa\\neq 0$ and $\\Box{A}$ is operator in Minkowski space $\\mathbb{R}^{1+3}$. The arises naturally when considering Yang–Mills–Higgs equations with Mexican hat type potentials. Our proof exploits mic...

As Schneider [50] observes, the classical Brunn-Minkowski theory had its origin at the turn of the 19th into the 20th century, when Minkowski joined a method of combining convex bodies (which became known as Minkowski addition) with that of ordinary volume. One of the core concepts that Minkowski introduced within the Brunn-Minkowski theory is that of projection body (precise definitions to fol...

In [F] Firey extended the notion of the Minkowski sum, and introduced, for each real p, a new linear combination of convex bodies, that he called p-sums. Lutwak [Lu2], [Lu3] showed that these Firey sums lead to a Brunn-Minkowski theory for each p ≥ 1. He introduced the notions of p-mixed volume, p-surface area measure, and proved an integral representation and inequalities for p-mixed volumes, ...

In this talk I review the issues of supersymmetry breaking and radion stabilization in a five dimensional theory compactified on the Z 2 orbifold. Supersymmetry breaking by Scherk-Schwarz boundary conditions is interpreted as spontaneous breaking of local supersymmetry by the Hosotani mechanism. The auxiliary field responsible for spontaneous supersymmetry breaking is inside the five-dimensiona...

It is shown that max-stable random vectors in [0,∞)d with unit Fréchet marginals are in one to one correspondence with convex sets K in [0,∞)d called max-zonoids. The max-zonoids can be characterised as sets obtained as limits of Minkowski sums of cross-polytopes or, alternatively, as the selection expectation of a random crosspolytope whose distribution is controlled by the spectral measure of...

The study of Einstein equations leads naturally to Cauchy problems with initial data on hypersurfaces which closely resemble hyperboloids in Minkowski space-time, and with initial data with polyhomogeneous asymptotics, that is, with asymptotic expansions in terms of powers of ln r and inverse powers of r. Such expansions also arise in the conformal method for analysing wave equations in odd spa...