相关论文: Multiplicities for Strongly Tempered Spherical Var…
We study smooth projective complex varieties with ample cotangent bundle. Our main result is that in an abelian variety of dimension n, a complete intersection of at least n/2 general hypersurfaces of sufficiently high degrees has ample…
Hyperuniform particle arrangements are characterized by a local number variance that grows more slowly than the volume of the observation window. We generalize this concept to describe particle systems in which particles carry weights:…
Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials.…
The concept of typical and weighted typical spherical faces for tessellations of the $d$-dimensional unit sphere, generated by $n$ independent random great hyperspheres distributed according to a non-degenerate directional distribution, is…
The affine Grassmannian associated to a reductive group $\mathbf{G}$ is an affine analogue of the usual flag varieties. It is a rich source of Poisson varieties and their symplectic resolutions. These spaces are examples of conical…
In this paper we construct a spectral sequence computing a modified version of morphic cohomology of a toric variety (even when it is singular) in terms of combinatorial data coming from the fan of the toric variety.
Strong Feller property and irreducibility are study for a class of non-linear monotone stochastic partial differential equations with multiplicative noise. H\"older continuity of the associated Markov semigroups are discussed in some…
We prove the uniqueness, up to diffeomorphism, of symplectically aspherical fillings of the unit cotangent bundle of odd-dimensional spheres. As applications, we first show the non-existence of exact symplectic cobordisms between some…
We have adapted Coupled Escape Probability, a new exact method of solving radiative transfer problems, for use in asymmetrical spherical situations. Our model is intended specifically for use in modeling optically thick cometary comae,…
We revisit the problem of local persistence in directed percolation, reporting improved estimates of the persistence exponent in 1+1 dimensions, discovering strong corrections to scaling in higher dimensions, and investigating the mean…
Producing dense and homogeneous powder layers with smooth free surface is challenging in additive manufacturing, as interparticle cohesion can strongly affect the powder packing structure and therefore influence the quality of the end…
We prove some fundamental structural results for spherical varieties in arbitrary characteristic. In particular, we study Luna's two types of localization and use it to analyze spherical roots, colors and their interrelation. At the end, we…
We propose two families of relative trace formula comparisons in the study of relative Langlands duality conjectured by Ben-Zvi--Sakellaridis--Venkatesh. This allows us to incorporate numerous relative trace formula comparisons studied…
Packing density is a permutation occurrence statistic which describes the maximal number of permutations of a given type that can occur in another permutation. In this article we focus on containment of sets of permutations. Although this…
We study semantic and syntactic properties of spherical orders and their elementary theories, including finite and dense orders and their theories. It is shown that theories of dense $n$-spherical orders are countably categorical and…
For a given irreducible projective variety $X$, the closure of the set of all hyperplanes containing tangents to $X$ is the projectively dual variety $X^{\vee}$. We study the singular locus of projectively dual varieties of certain…
A dense cloud of atoms with randomly changing positions exhibits coherent and incoherent scattering. We show that an atomic cloud of subwavelength dimensions can be modeled as a single scatterer where both coherent and incoherent components…
Our main aim is to provide a uniform geometric characterization of the analogues over arbitrary fields of the four complex Severi varieties, i.e.~the quadric Veronese varieties in 5-dimensional projective spaces, the Segre varieties in…
We generally study the density of eigenvalues in unitary ensembles of random matrices from the recurrence coefficients with regularly varying conditions for the orthogonal polynomials. First we calculate directly the moments of the density.…
The characteristic variety plays an important role in the analysis of the solution space of partial differential equations and exterior differential systems. This article studies the linear span of this variety, measuring its dimension via…