Related papers: Criteria for Morin singularities into higher dimen…
This paper investigates the equivalence reduction for several classes of multivariate polynomial matrices and their Smith forms, establishing some criteria for such reduction. In particular, we employ algebra isomorphisms as a key tool to…
We review the vacuum solutions of Einstein's equations in higher dimensions known as Myers-Perry metrics. In many respects, these solutions describing spinning black holes admit the same remarkable properties as the standard Kerr black hole…
It is shown that, by letting wavenumbers and frequencies complex in Hirota's bilinear method, new classes of exact solutions of soliton equations can be obtained systematically. They include not only singular or N-homoclinic solutions but…
Soliton equations in 2+1 and their 1+1 = 2+0 reductions are considered.
We provide new criteria for the integrality and birationality of an extension of graded algebras in terms of the general notion of polar multiplicities of Kleiman and Thorup. As an application, we obtain a new criterion for when a module is…
We introduce a class of overdetermined systems of partial differential equations of finite type on (pseudo)-Riemannian manifolds that we call the generalised Ricci soliton equations. These equations depend on three real parameters. For…
We prove some conditions for the existence of higher dimensional algebraic fibering of group extensions. This leads to various corollaries on incoherence of groups and some geometric examples of algebraic fibers of type $F_n$ but not…
There is an optimal way to increase certain cardinal invariants of the continuum.
In this paper, we give the Assouad dimension formula and the upper bound of the lower dimension for homogeneous Moran sets under the condition $\sup_{k\ge 1}\{n_{k}\}<+\infty$. We also give the Assouad spectrum and the lower spectrum…
We extend the definition of $\mathcal{A}$-discriminant varieties, and Kapranov's parametrization of $\mathcal{A}$-discriminant varieties, to complex exponents. As an application, we study the special case where $\mathcal{A}$ is a fixed real…
We provide explicit bounds on the difference of heights of isogenous Drinfeld modules. We derive a finiteness result in isogeny classes. In the rank 2 case, we also obtain an explicit upper bound on the size of the coefficients of modular…
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…
In this talk we discuss a class of Feynman integrals, which can be expressed to all orders in the dimensional regularisation parameter as iterated integrals of modular forms. We review the mathematical prerequisites related to elliptic…
We prove upper bounds on the face numbers of simplicial complexes in terms on their girths, in analogy with the Moore bound from graph theory. Our definition of girth generalizes the usual definition for graphs.
In this paper we give methods to classify the central singularities of Cayley-Hamilton smooth orders up to smooth equivalence in arbitrary central dimension. We prove that there is just one type in dimension 3 (the conifold singularity),…
We study in this paper some criterions to get polarized morphisms between abelian varieties. We deduce explicit dynamical systems with particular intersection properties.
We algebraically classify some higher dimensional spacetimes, including a number of vacuum solutions of the Einstein field equations which can represent higher dimensional black holes. We discuss some consequences of this work.
Matrix norms can be used to measure the "distance" between two matrices which translates naturally to the problem of calculating the unitary deviation of the neutrino mixing matrices. Variety of matrix norms opens a possibility to measure…
We define four different kinds of multiplicity of an invariant algebraic curve for a given polynomial vector field and investigate their relationships. After taking a closer look at the singularities and at the line of infinity, we improve…
Using ideas employed in higher dimensional gravity, non-expanding, weakly isolated and isolated horizons are introduced and analyzed in 2+1 dimensions. While the basic definitions can be taken over directly from higher dimensions, their…