We describe two simple obstructions to the existence of Ricci–flat Kähler cone metrics on isolated Gorenstein singularities or, equivalently, to the existence of Sasaki–Einstein metrics on the links of these singularities. In particular, this also leads to new obstructions for Kähler–Einstein metrics on Fano orbifolds. We present several families of hypersurface singularities that are obstructe...

We consider power-like corrections in QCD which can be viewed as power surpressed infrared singularities. We argue that the presence of these singularities depends crucially on the energy resolution. In case of poor energy resolution, i.e., inclusive cross sections, there are constraints on in-frared singularities expressed by the Kinoshita-Lee-Nauenberg (KLN) theorem. We rewrite the theorem in...

Repulsive singularities (“repulsons”) in extended supergravity theories are investigated. These repulsive singularities are related to attractive singularities (“black holes”) in moduli space of extended supergravity vacua. In order to study these repulsive singularities a scalar test-particle in the background of a repulson is investigated. It is shown, using a partial wave expansion, that the...

We introduce a general characterisation of sudden cosmological singularities and investigate the classical stability of homogeneous and isotropic cosmological solutions of all curvatures containing these singularities to small scalar, vector, and tensor perturbations using gauge invariant perturbation theory. We establish that sudden singularities at which the scale factor, expansion rate, and ...

Previously, we introduced a duality transformation for Euler G– Frobenius algebras. Using this transformation, we prove that the simple A,D,E singularities and Pham singularities of coprime powers are mirror self– dual where the mirror duality is implemented by orbifolding with respect to the symmetry group generated by the grading operator and dualizing. We furthermore calculate orbifolds and ...

A canonical construction of a balanced big Cohen-Macaulay algebra for a domain of finite type over C is obtained by taking ultraproducts of absolute integral closures in positive characteristic. Among the applications are a new tight closure characterization of rational singularities in characteristic zero, and a necessary condition for Q-Gorenstein logterminal singularities. In particular, it ...

We consider the time-harmonic eddy current problem in its electric formulation where the conductor is a polyhedral domain. By proving the convergence in energy, we justify in what sense this problem is the limit of a family of Maxwell transmission problems: Rather than a low frequency limit, this limit has to be understood in the sense of BOSSAVIT [11]. We describe the singularities of the solu...

I describe an extension of a portion of the theory of the Laplace operator on compact riemannian manifolds to certain spaces with singularities. Although this approach can be extended to include quite general spaces, this paper will confine itself to the case of manifolds with cone-like singularities. These singularities are geometrically the simplest possible, but they already serve to illustr...

In the present paper, we determine the conditions necessary for the generation of phase singularities in the far-field by a phase bar or a trench. The ultimate goal of our work is to link object parameters to a topological distribution of pairs of singularities. We apply scalar theory and show that objects smaller than the diffraction limit are not capable of generating singularities. Supplemen...

We prove microlocal properties of a generalized Radon transform that integrates over lines in R3 with directions parallel to a fairly arbitrary curve on the sphere. This transform is the model for problems in slant-hole SPECT and conical-tilt electron microscopy, and our results characterize the microlocal mapping properties of the SPECT reconstruction operator developed and tested by Quinto, B...