We show the existence of timelike naked singularities which are not hidden by a horizon and which are associated to spherically symmetric (noncompact) matter sources extending from r = 0 to r = ∞. Our asymptotically flat solutions do represent observable timelike naked singularities where the scalar curvature R and volume mass density ρ(r) are both singular at r = 0. To finalize we explain the ...

We recall the form factors f (j) N,N corresponding to the λ-extension C(N,N ;λ) of the two-point diagonal correlation function of the Ising model on the square lattice and their associated linear differential equations which exhibit both a “Russian-doll” nesting, and a decomposition of the linear differential operators as a direct sum of operators (equivalent to symmetric powers of the differen...

Divisorial contractions to singularities, defined by equations xy + zn + un = 0 n ≥ 3 and xy + z + u = 0 are classified. The problem of birational classification of algebraic varieties is highly interconnected with the problem of description of singularities on them. One of the most important class of three-dimensional singularities is terminal singularities, which arise within minimal models p...

This paper covers some of the current techniques and issues involed in performing numerical simulations of the formation of singularities. Numerical simulations of general gravitational singularities 2

The equations of hydrodynamics are nonlinear partial differential equations, so they include the possibility of forming singularities in finite time. This means that hydrodynamic fields become infinite or at least non-smooth at points, lines, or even fractal objects. This mathematical possibility is the price one has to pay for the enormous conceptual simplification a continuum theory brings fo...

An overview is provided of the singularity theorems in cosmological contexts at a level suitable for advanced graduate students. The necessary background from tensor and causal geometry to understand the theorems is supplied, the mathematical notion of a cosmology is described in some detail and issues related to the range of validity of general relativity are also discussed. ∗To be published i...

We study Thom polynomials associated with Lagrange singularities. We expand them in the basis of Q̃-functions. This basis plays a key role in the Schubert calculus of isotropic Grassmannians. We prove that the Q̃-function expansions of Thom polynomials of Lagrange singularities have always nonnegative coefficients. This is an analog of a result on Thom polynomials of mapping singularities and Sch...

We prove an “Earthquake Theorem” for closed hyperbolic surfaces with cone singularities where the total angle is less than π: the action of the space of measured laminations on Teichmüller space by left earthquakes is simply transitive. This is strongly related to another result: the space of “globally hyperbolic” AdS manifolds with cone singularities (of given angle) along time-like geodesics ...

We study the occurrence, visibility, and curvature strength of singularities in dust-containing Szekeres spacetimes (which possess no Killing vectors) with a positive cosmological constant. We find that such singularities can be locally naked, Tipler strong, and develop from a non-zero-measure set of regular initial data. When examined along timelike geodesics, the singularity’s curvature stren...