Research
Research
Research
Research
130+ open-access research outputs.
Given $n$ lines in general position in the plane, how many bounded triangular faces can the arrangement have? We construct a straight-line affine arrangement of $19$ lines satisfying the conditions of…
In this paper, we study Hardy-type uncertainty principles and unique continuation properties for linear covariant Schrodinger equations with variable coefficients in the presence of bounded electric a…
Polylab is a MATLAB toolbox for multivariate polynomial scalars and polynomial matrices with a unified symbolic-numeric interface across CPU and GPU-oriented backends. The software exposes three align…
Affine normal directions provide intrinsic affine-invariant descent directions derived from the geometry of level sets. Their practical use, however, has long been hindered by the need to evaluate thi…
Corresponding to a hyperbolic system $(V, p, e)$, where $V$ is a real finite-dimensional vector space and $p$ is a hyperbolic polynomial of degree $n$ in the direction $e$, we consider the eigenvalue …
We prove that for any dominant cocharacter $\mu$ and any parahoric level $K$, the augmented admissible set $\widehat{\Adm(\mu)^K}$ in the Iwahori-Weyl group is dual EL-shellable. This resolves a conje…
We compute the volumes of convex bodies that are given by inequalities of concave polynomials. These volumes are found to arbitrary precision thanks to the representation of periods by linear differen…
In this article, we establish a nearly sharp localized weighted inequality related to Gagliardo and Sobolev seminorms, respectively, with the sharp $A_1$-weight constant or with the specific $A_p$-wei…
The main purpose of this article is to show that the special Newton polygon map from the stack of p-adic shtukas to the stack of G-bundles on the Fargues--Fontaine curve is representable in diamonds a…
We show that tessellations of hyperbolic space by isometry-invariant Poisson processes of $(d-1)$-dimensional hyperplanes do not have an unbounded cell at the critical intensity. This extends a result…
We investigate the Arens products on the second duals of convolution algebras associated with Ch\'{e}bli--Trim\`{e}che hypergroups, particularly focusing on the left and right topological centres of $…
For computational convenience, a Prony series approximation of the stretched exponential relaxation function of homogeneous glasses has been proposed (J. Mauro, Y. Mauro, 2018), which is the extended …
In this article, we study the growth of higher-order Sobolev norms for solutions to the defocusing cubic nonlinear Schr\"odinger equation with harmonic potential in dimensions $d=2,3$, \begin{align}\l…
We study morphisms of schemes $f : X \to S$ which are locally of finite type. We present conditions under which there exists a morphism $g : S'\to X$ of $S$--schemes such that $f \circ g $ is the cano…
Given two variable exponent Muckenhoupt weights $w\in A_{p(\cdot)}$ and $w_1\in A_{p_1(\cdot)}$, we prove that for all small enough $\theta>0,$ there holds that $w_0\in A_{p_0(\cdot)},$ where the weig…
This paper investigates the boundedness of a broad class of operators within the framework of generalized Morrey-Banach function spaces. This class includes multilinear operators such as multilinear $…
We show that in three different critical regimes, the masses of the connected components of rank-2 multiplicative random graph converge to lengths of excursions of a thinned L\'{e}vy process, perhaps …
It is the purpose of this article to compare various concepts of ``function spaces''. In particular we compare notions of the concept of Banach Function Spaces (in the spirit of Luxemburg-Zaanen) to t…
We demonstrate that the submonoid membership problem and the rational subset membership problem are equivalent in Artin groups. Both these problem are undecidable in a given Artin group if and only if…
We study several natural decision problems in braid groups and Artin groups. We classify the Artin groups with decidable submonoid membership problem in terms of the non-existence of certain forbidden…
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