We generalize, to any space-time dimension, the unitarity bounds of highest weight UIR’s of the conformal groups with Lie algebras so(2, d). We classify gauge theories invariant under so(2, d), both integral and half-integral spins. A similar analysis is carried out for the algebras so(2n). We study new unitary modules of the conformal algebra in d > 4, that have no analogue for d ≤ 4 as they c...

We have recently proposed an alternative picture for the physics at the scale of gauge coupling unification, where the unified symmetry is realized in higher dimensions but is broken locally by a symmetry breaking defect. Gauge coupling unification, the quantum numbers of quarks and leptons and the longevity of the proton arise as phenomena of the symmetrical bulk, while the lightness of the Hi...

I prove, answering a question of Zilber, that if M is an algebraic variety, dimM > 1, and (M, . . .) is a strongly minimal structure with atomic relations definable in the Zariski language on M , then M is locally modular.

We show that in dimensions d > 3 , aperiodic tilings can naturally avoid more symmetries than just translations.

Let A(t) denote the cluster produced by internal diffusion limited aggregation (internal DLA) with t particles in dimension d ≥ 3. We show that A(t) is approximately spherical, up to an O( √ log t) error. In the process known as internal diffusion limited aggregation (internal DLA) one constructs for each integer time t ≥ 0 an occupied set A(t) ⊂ Zd as follows: begin with A(0) = ∅ and A(1) = {0...

A theorem of Glasner says that if X is an infinite subset of the torus T, then for any > 0, there exists an integer n such that the dilation nX = {nx : x ∈ T} is -dense (i.e, it intersects any interval of length 2 in T). Alon and Peres provided a general framework for this problem, and showed quantitatively that one can restrict the dilation to be of the form f(n)X where f ∈ Z[x] is not constan...

We study cubature formulas for d-dimensional integrals with an arbitrary symmetric weight function of tensor product form. We present a construction that yields a high polynomial exactness: for fixed degree l = 5 or l = 7 and large dimension d the number of knots is only slightly larger than the lower bound of Möller and much smaller compared to the known constructions. We also show, for any od...

We calculate the first three Gilkey-DeWitt (heat-kernel) coefficients, a0, a1 and a2, for massive particles having the spins of most physical interest in n dimensions, including the contributions of the ghosts and the fields associated with the appropriate generalized Higgs mechanism. By assembling these into supermultiplets we compute the same coefficients for general supergravity theories, an...

This is a survey of higher-dimensional Kleinian groups, i.e., discrete isometry groups of the hyperbolic n-space H for n ≥ 4. Our main emphasis is on the topological and geometric aspects of higher-dimensional Kleinian groups and their contrast with the discrete groups of isometry of H. To the memory of Sasha Reznikov

Warped configurations admitting pairs of gravitating defects are analyzed. After devising a general method for the construction of multidefects, specific examples are presented in the case of higher-dimensional Einstein-Hilbert gravity. The obtained profiles describe diverse physical situations such as (topological) kink-antikink systems, pairs of non-topological solitons and bound configuratio...