Related papers: Intersecting Legendrians and blowups
We study germs of holomorphic distributions with "separated variables'. In codimension one, a well know example of this kind of distribution is given by the canonical contact structure on $\mathbb{P}^{2m+1}$ . Another example is the Darboux…
Motivated by two Legendre-type formulas for overpartitions, we derive a variety of their companions as Legendre theorems for overpartition pairs. This leads to equalities of subclasses of overpartitions and overpartition pairs.
This paper considers a family of distributions constructed by a stochastic mixture of the order statistics of a sample of size two. Various properties of the proposed model are studied. We apply the model to extend the exponential and…
We introduce and study new transformations between two functions satisfying some basic growth properties and generalize the known lower and upper Legendre conjugate (or envelope). We also investigate how these transformations modify…
Using class field theory, we prove a restriction on the intersection of the maximal abelian extensions associated with different number fields. This restriction is then used to improve a result of Rosen and Silverman about the linear…
The asymmetric scattering between wobblers and kinks in the standard $\phi^4$ model is numerically investigated in two different scenarios. First, the collision between wobblers with opposite phase is analyzed. Here, a destructive…
Differential graded algebra invariants are constructed for Legendrian links in the 1-jet space of the circle. In parallel to the theory for R^3, Poincare-Chekanov polynomials and characteristic algebras can be associated to such links. The…
We give a combinatorial description of the Legendrian differential graded algebra associated to a Legendrian knot in PxR, where P is a punctured Riemann surface. As an application we show that for any integer k and any homology class h in…
We study random subcube intersection graphs, that is, graphs obtained by selecting a random collection of subcubes of a fixed hypercube $Q_d$ to serve as the vertices of the graph, and setting an edge between a pair of subcubes if their…
In a series of papers the authors introduced the so-called blown-up intersection cochains. These cochains are suitable to study products and cohomology operations of intersection cohomology of stratified spaces. The aim of this paper is to…
The discovery of Exoplanetary Systems has challenged some of the theories of planet formation, which assume unperturbed evolution of the host star and its planets. However, in star clusters the interactions with flyby stars and binaries may…
In this short note we provide the examples of pairs of closed, connected Legendrian non-isotopic Legendrian submanifolds $(\Lambda_{-}, \Lambda_{+})$ of the $(4n+1)$-dimensional contact vector space, $n>1$, such that there exist Lagrangian…
This paper is devoted to abelian varieties arising from generalized Legendre curves. In particular, we consider their corresponding Galois representations, periods, and endomorphism algebras. For certain one parameter families of…
We study segregation and stratification of mixtures of grains differing in size, shape and material properties poured in two-dimensional silos using a microscopic lattice model for surface flows of grains. The model incorporates the…
We use Picard-Lefschetz theory to prove a new formula for intersection numbers of twisted cocycles associated to a given arrangement of hyperplanes. In a special case when this arrangement produces the moduli space of punctured Riemann…
Score-matching generative models have proven successful at sampling from complex high-dimensional data distributions. In many applications, this distribution is believed to concentrate on a much lower $d$-dimensional manifold embedded into…
There is a remarkable type of field of two-planes special to four dimensions known as an Engel distributions. They are the only stable regular distributions besides the contact, quasi-contact and line fields. If an arbitrary two-plane field…
The repartition of dense orbits of $\textrm{SL}(2,\dr Z)$ in the euclidean plane is described by Ledrappier and Nogueira. We describe here the specific patterns one can see by experimentation, linking it to diophantine approximation theory.
We observe strongly dissimilar scattering from two types of edges in hexagonal quasi-monocrystalline gold flakes with thicknesses around 1 micron. We identify as the origin the interference between a direct, quasi-specular scattering and an…
We describe an optical technique based on the statistical analysis of the random intensity distribution due to the interference of the near-field scattered light with the strong transmitted beam. It is shown that, from the study of the…