Regular triangulations of products of lattice polytopes are constructed with the additional property that the dual graphs of the triangulations are bipartite. Such triangulations are instrumental in deriving lower bounds for the number of real roots of certain sparse polynomial systems by recent results of Soprunova and Sottile (Adv. Math., to appear). Special attention is paid to the cube case.

Causal variational principles on measure spaces are introduced. General existence results are proved. It is shown in examples that minimizers need not be unique. Counter examples to compactness are discussed. The existence results are applied to variational principles formulated in indefinite inner product spaces.

We continue to develop an obstruction theory for embedding 2–spheres into 4–manifolds in terms of Whitney towers. The proposed invariants take values in certain graded abelian groups generated by labelled trivalent trees, well known from the 3–dimensional theory of finite type invariants. Surprisingly, the same exact relations arise in 4 dimensions, for example the Jacobi (or IHX) relation come...

We introduce a new representation of the paths of the Forrester-Baxter RSOS models which represents the states of the irreducible modules of the minimal models M(p ′ , p). This representation is obtained by transforming the RSOS paths, for the cases p ≥ 2p ′ − 1, to new paths for which horizontal edges are allowed at certain heights. These new paths are much simpler in that their weight is noth...

— An upper bound of the expected order of magnitude is established for the number of Q-rational points of bounded height on Châtelet surfaces defined over Q.

SPOrt is an ASI–funded experiment specifically designed to measure the sky polarization at 22, 32 and 90 GHz, which was selected in 1997 by ESA to be flown on the International Space Station. Starting in 2006 and for at least 18 months, it will be taking direct and simultaneous measurements of the Stokes parameters Q and U at 660 sky pixels, with FWHM = 7◦. Due to development efforts over the p...

We investigate the second-order correlation function of the characteristic polynomial of a sample covariance matrix. Starting from an explicit formula for a generating function, we re-obtain several well-known kernels from random matrix theory.

Without additional resources, it is often impossible to transform one entangled quantum state into another with local quantum operations and classical communication. Jonathan and Plenio [Phys. Rev. Lett. 83, 3566(1999)] presented an interesting example showing that the presence of another state, called a catalyst, enables such a transformation without changing the catalyst. They also pointed ou...

We first introduce an invariant index for G-equivariant elliptic differential operators on a locally compact manifold M admitting a proper cocompact action of a locally compact group G. It generalizes the Kawasaki index for orbifolds to the case of proper cocompact actions. Our invariant index is used to show that an analog of the Guillemin-Sternberg geometric quantization conjecture holds if M...