Fundamental theories of quantum gravity such as supergravity include a four form field strength which contributes to the cosmological constant. The inclusion of such a field into our theory of open inflation [1] allows an anthropic solution to the cosmological constant problem in which cosmological constant gives a small but non-negligible contribution to the density of today's universe. We inc...

this paper is a slightly revised version of an introduction into singularity theory corresponding to a series of lectures given at the ``advanced school and conference on homological and geometrical methods in representation theory'' at the international centre for theoretical physics (ictp), miramare - trieste, italy, 11-29 january 2010. we show how to associate to a triple of positive integer...

Gravitational collapse is one of the most fruitful subjects in gravitational physics. It is well known that singularity formation is inevitable in complete gravitational collapse. It was conjectured that such a singularity should be hidden by horizons if it is formed from generic initial data with physically reasonable matter fields. Many possible counterexamples to this conjecture have been pr...

Hallin and Ley (2012) investigate and fully characterize the Fisher singularity phenomenon in univariate and multivariate families of skew-symmetric distributions. This paper proposes a refined analysis of the (univariate) Fisher degeneracy problem, showing that it can be more or less severe, inducing n (“simple singularity”), n (“double singularity”), or n (“triple singularity”) consistency ra...

We study the behavior of geodesies passing through a point singularity of a Riemannian manifold. In particular, we show that if the curvature does not blow up too rapidly near the singularity, then the singularity is at worst an orbifold singularity. The idea is to construct the exponential map centered at a singularity. Since there is no tangent space at the singularity, a surrogate is needed....

We construct a new class of plane-symmetric solutions possessing a curvature singularity which is null and weak, like the spacetime singularity at the Cauchy horizon of spinning (or charged) black holes. We then analyse the stability of this singularity using a rigorous non-perturbative method. We find that within the framework of (linearly-polarized) plane-symmetric spacetimes this type of nul...

Fixed a point O on a non-singular surface S and a complete mO-primary ideal I in OS,O , the curves on the surface X = BlI (S) obtained by blowing-up I are studied in terms of the base points of I. Criteria for the principality of these curves are obtained. New formulas for their multiplicity, intersection numbers and order of singularity at the singularities of X are given. The semigroup of bra...

We study the homogeneous Dirichlet problem for some elliptic equations with a first order term b(u,Du) which is quadratic in the gradient variable and singular in the u variable at a positive point. Moreover, the gradient term we consider, changes its sign at the singularity. Dealing with an appropriate concept of solution that gives sense to the equation at the singularity, we prove existence ...

We consider solutions to the Euler equations in the whole space from a certain class, which can be characterized, in particular, by finiteness of mass, total energy and momentum. We prove that for a large class of right-hand sides, including the viscous term, such solutions, no matter how smooth initially, develop a singularity within a finite time. We find a sufficient condition for the singul...