Related papers: Equisingularity and EIDS
For an isolated hypersurface singularity which is neither simple nor simple elliptic, it is shown that there exists a distinguished basis of vanishing cycles which contains two basis elements with an arbitrary intersection number. This…
We study the equation for improper (parabolic) affine spheres from the view point of contact geometry and provide the generic classification of singularities appearing in geometric solutions to the equation as well as their duals. We also…
Seminar held at JINR, Dubna, May 15, 2012. In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities - with smooth but degenerate metric - which,…
We study the relationship between singularities of finite-dimensional integrable systems and singularities of the corresponding spectral curves. For the large class of integrable systems on matrix polynomials, which is a general framework…
In a previous work [I. Rodnianski and Y. Shlapentokh-Rothman, Naked Singularities for the Einstein Vacuum Equations: The Exterior Solution, arXiv:1912.08478] we constructed solutions to the Einstein vacuum equations in 3+1 dimensions which…
Linear combinations of exponentials $e^{i\lambda_kt}$ in the case where the distance between some points $\lambda_k$ tends to zero are studied. D. Ullrich has proved the basis property of the divided differences of exponentials in the case…
There are two well known tasks, related to Newton polyhedra: to study invariants of singularities in terms of their Newton polyhedra, and to describe Newton polyhedra of resultants and discriminants. We introduce so called resultantal…
Francesco Severi showed that equisingular families of plane nodal curves are T-smooth, i.e. smooth of the expected dimension, whenever they are non-empty. For families with more complicated singularities this is no longer true. Given a…
We prove strong well-posedness for a class of stochastic evolution equations in Hilbert spaces H when the drift term is Holder continuous. This class includes examples of semilinear stochastic damped wave equations which describe elastic…
In this work we investigate the stability and instability properties of a class of naked singularity spacetimes. The first rigorous study of naked singularity formation in the spherically symmetric Einstein-scalar field system was due to…
Singularities of even smooth functions are studied. A classification of singular points which appear in typical parametric families of even functions with at most five parameters is given. Bifurcations of singular points near a caustic…
This paper develops a construction of families of $ U(1)^{n-2} $-invariant special Lagrangian $ n $-folds in $ \mathbb{C}^{n} $, extending the analytic framework introduced by Joyce ($ n = 3 $) to arbitrary dimension. By reducing the…
This thesis deals with General Probabilistic Theories (GPTs) and Entanglement Structures (ESs). An ES is a possible structure of a quantum composite system in GPTs, which is not uniquely determined as the Standard Entanglement Structure…
We introduce a new isomorphism invariant for generalized Baumslag-Solitar (GBS) groups, which we call the limit angle. Unlike previously known invariants, which are primarily algebraic, the limit angle admits a dynamical interpretation,…
We study the fully discrete elliptic integrable model Q4 and its immediate trigonometric and rational counterparts (Q3, Q2 and Q1). Singular boundary problems for these equations are systematised in the framework of global singularity…
The problem of determining whether a diagonally dominant matrix is singular or nonsingular is a classical topic in matrix theory. This paper develops necessary and sufficient conditions for the singularity or nonsingularity of diagonally…
We introduce a novel method for proving ergodicity for skew products of interval exchange transformations (IETs) with piecewise smooth cocycles having singularities at the ends of exchanged intervals. This approach is inspired by…
We present a detailed study of a new mathematical object in $\mathrm{E}_{6(6)}\times \mathbb{R}^{+}$ generalised geometry called an `exceptional complex structure' (ECS). It is the extension of a conventional complex structure to one that…
The method of imsets, introduced by Studen\'y, provides a geometric and combinatorial description of conditional independence statements. Elementary conditional independence statements over a finite set of discrete random variables…
The existence of stationary distributions to distribution dependent stochastic differential equations are investigated by using the ergodicity of the associated decoupled equation and the Schauder fixed point theorem. By using Zvonkin's…