We describe the construction of the genus-zero parts of conformal field theories in the sense of G. Segal from representations of vertex operator algebras satisfying certain conditions. The construction is divided into four steps and each step gives a mathematical structure of independent interest. These mathematical structures are intertwining operator algebras, genus-zero modular functors, ge...

For a weakly pseudo-Hermitian linear operator, we give a spectral condition that ensures its pseudo-Hermiticity. This condition is always satisfied whenever the operator acts in a finite-dimensional Hilbert space. Hence weak pseudo-Hermiticity and pseudo-Hermiticity are equivalent in finite-dimensions. This equivalence extends to a much larger class of operators. Quantum systems whose Hamiltoni...

Let T : C(S) → C(S) be a bounded linear operator. We present a necessary and sufficient condition for the so-called Daugavet equation ‖Id+ T ‖ = 1 + ‖T ‖ to hold, and we apply it to weakly compact operators and to operators factoring through c0. Thus we obtain very simple proofs of results by Foiaş, Singer, Pe lczyński, Holub and others. If E is a real Banach space, let us say that an operator ...

We study 22 systems of variational inequalities which are only weakly elliptic; in particular, these systems are not necessarily monotone. The prototype diierential operator is the (vector-valued) p-Laplacian. We prove, under certain conditions, the existence of solutions to the unilateral obstacle problem. In addition, we address the question of determining function spaces on which the p-Lapla...

In this article we discuss some general results on the covariant Picard groupoid in the context of differential geometry and interpret the problem of lifting Lie algebra actions to line bundles in the Picard groupoid approach.

We describe all of the smooth complete toric threefolds of Picard number 5 with no nontrivial nef line bundles, and show that no such examples exist with Picard number less than 5.

A Banach space E has the Grothendieck property if every (linear bounded) operator from E into c0 is weakly compact. It is proved that, for an integer k > 1, every k-homogeneous polynomial from E into c0 is weakly compact if and only if the space P(kE) of scalar valued polynomials on E is reflexive. This is equivalent to the symmetric k-fold projective tensor product of E (i.e., the predual of P...

We propose an extension to the double iteration method, the Multipower Defect Correction method, which is used to refine approximate eigenelements of integral operators. It consists of an inner/outer iteration where, inside a defect correction iteration, p steps of a power iteration are used. The approximate inverse used in the defect correction is built with an approximation to the reduced res...

We study inversions of the jump operator on Π1 classes, combined with certain basis theorems. These jump inversions have implications for the study of the jump operator on the random degrees—for various notions of randomness. For example, we characterize the jumps of the weakly 2-random sets which are not 2-random, and the jumps of the weakly 1-random relative to 0′ sets which are not 2-random....