Related papers: Criteria for Morin singularities into higher dimen…
A monoid hypersurface is an irreducible hypersurface of degree d which has a singular point of multiplicity d-1. Any monoid hypersurface admits a rational parameterization, hence is of potential interest in computer aided geometric design.…
This paper is the first part of a two part paper which introduces the study of the Whitney Equisingularity of families of Symmetric determinantal singularities. This study reveals how to use the multiplicity of polar curves associated to a…
Optical singularities, which are positions within an electromagnetic field where certain field parameters become undefined, hold significant potential for applications in areas such as super-resolution microscopy, sensing, and…
We construct a category equivalent to the category $\mathbf{Mon}$ of monoids and monoid homomorphisms, based on categories with strict factorization systems. This equivalence is then extended to the category $\mathbf{Mon_s}$ of unital…
We consider a variational problem with boundary singularity and Dirichlet condition. We give a blow-up analysis for sequences of solutions of an equation with exponential nonlinearity. Also, we derive a compactness criterion under some…
Improving a result of Woodin, we identify some classes of individually consistent but mutually inconsistent generic large cardinal axioms.
We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.
Moran sets are a non-autonomous generalization of self-similar sets. In this paper, we study the quasi-Assouad and Assouad dimensions of Moran sets in $\mathbb{R}^{d}$. First we provide quasi-Assouad dimension formulae for Moran sets…
We consider possibly degenerate and singular elliptic equations in a possibly anisotropic medium. We obtain monotonicity results for the energy density, rigidity results for the solutions and classification results for the…
Let $R$ be a commutative noetherian ring. Denote by $\operatorname{mod} R$ the category of finitely generated $R$-modules and by $\operatorname{D^b}(R)$ the bounded derived category of $\operatorname{mod} R$. In this paper, we first…
We show the existence of an infinite family of finite-time singularities in isotropically expanding universes which obey the weak, strong, and dominant energy conditions. We show what new type of energy condition is needed to exclude them…
We argue that a certain distribution of matter in higher dimensions can provide the correct behaviour of gravity in four dimensions. Some explicit examples illustrating the idea are considered.
We give a normal form for families of 3-dimensional Poisson structures. This allows us to classify singularities with nonzero 1-jet and typical bifurcations. The Appendix contains corollaries on classification of families of integrable…
We study the poset of Hamiltonian tori for polygon spaces. We determine some maximal elements and give examples where maximal Hamiltonian tori are not all of the same dimension.
The symmetry classification method is applied to the string-like scalar fields in two-dimensional space-time. When the configurational space is three-dimensional and reducible we present the complete list of the systems admiting higher…
In this paper we use the comparison method for investigation of first order polynomial differential equations. We prove two comparison criteria for these equations. The proved criteria we use to obtain some global solvability criteria for…
We present a method for computing $\mathbb{A}^1$-homotopy invariants of singularity categories of rings admitting suitable gradings. Using this we describe any such invariant, e.g. homotopy K-theory, for the stable categories of…
We define sets of coulourings of the infinite discrete plane using monadic second order (MSO) formulas. We determine the complexity of deciding whether such a formula defines a subshift, parametrized on the quantifier alternation complexity…
In this paper, we study dimensions of some varieties, that were introduced recently by Kisin in order to prove modularity of some Galois representations. In fact, we mainly consider a special case for which we obtain an estimation of the…
We give a criterium of holomorphy for some type formal power series. This gives a stronger form of a Rothstein's type extension theorem for a particular ring of holomorphic functions.