Related papers: Lattice-Supported Splines on Polytopal Complexes
The description of the Paley-Wiener space for compactly supported smooth functions $C^\infty_c(G)$ on a semi-simple Lie group $G$ involves certain intertwining conditions that are difficult to handle. In the present paper, we make them…
The h^*-polynomial of a lattice polytope is the numerator of the generating function of the Ehrhart polynomial. Let P be a lattice polytope with h^*-polynomial of degree d and with linear coefficient h^*_1. We show that P has to be a…
We analyze CP symmetry in symplectic modular-invariant supersymmetric theories. We show that for genus $g\ge 3$ the definition of CP is unique, while two independent possibilities are allowed when $g\le 2$. We discuss the transformation…
A piecewise Chebyshevian spline space is good for design when it possesses a B-spline basis and this property is preserved under knot insertion. The interest in such kind of spaces is justified by the fact that, similarly as for polynomial…
Given a polynomial map $\psi:S^m\to \mathbb{R}^k$ with components of degree $d$, we investigate the structure of the semialgebraic set $Z\subseteq S^m$ consisting of those points where $\psi$ and its derivatives satisfy a given list of…
We describe the support of $F$-finite $F$-modules over polynomial rings $R$ of prime characteristic. Our description yields an algorithm to compute the support of such modules; the complexity of our algorithm is also analyzed. To the best…
We investigate the density of compactly supported smooth functions in the Sobolev space $W^{k,p}$ on complete Riemannian manifolds. In the first part of the paper, we extend to the full range $p\in [1,2]$ the most general results known in…
Inspired by constructions over the complex numbers of Dolgachev and Alexeev-Engel, we define moduli stacks $\mathcal{M}_{(L,\mathcal{A})/\mathbb{Z}}$ of lattice-polarized K3 surfaces over arbitrary bases, paying particular attention to the…
We prove a sharp upper bound on the number of boundary lattice points of a rational polygon in terms of its denominator and the number of interior lattice points, generalizing Scott's inequality. We then give sharp lower and upper bounds on…
We study and simulate N=2 supersymmetric Wess-Zumino models in one and two dimensions. For any choice of the lattice derivative, the theories can be made manifestly supersymmetric by adding appropriate improvement terms corresponding to…
The higher fusion level logarithmic minimal models LM(P,P';n) have recently been constructed as the diagonal GKO cosets (A_1^{(1)})_k oplus (A_1^{(1)})_n / (A_1^{(1)})_{k+n} where n>0 is an integer fusion level and k=nP/(P'-P)-2 is a…
We study properties of compactly supported $p$-adic pro-\'etale cohomology of smooth partially proper rigid analytic varieties. In particular, we prove a comparison theorem, in a stable range, with compactly supported syntomic cohomology,…
Let $k$ be an algebraically closed field. Fix integers $n$ and $b$ with $n\geq 3$ and $1\leq b\leq n-1.$ Let $T^d_k$ be the moduli space of hypersurfaces $[F]$ in $\mathbb{P}^n_k$ of degree $l$ whose singular locus contains a subscheme of…
In Part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules. The spherical functions are taking values in the…
We suggest a new method of basis construction for the kernel of a linear form on the Laurent polynomial module related to multivariate wavelets, and demonstrate its applications to box spline prewavelets, leading to small mask supports for…
This paper is a contribution to piecewise linear (PL) symplectic topology. We define the notion of PL symplectic manifold as being a combinatorial manifold endowed with a piecewise constant Whitney symplectic form and investigate possible…
We prove that if a simplicial complex is shellable, then the intersection lattice for the corresponding diagonal arrangement is homotopy equivalent to a wedge of spheres. Furthermore, we describe precisely the spheres in the wedge, based on…
We apply the techniques developed by Marcus, Spielman and Srivastava, working with principal submatrices in place of rank $1$ decompositions to give an alternate proof of their results on restricted invertibility. We show that one can find…
We consider the $Sp(4)$ gauge theory coupled to $N_f=2$ fundamental and $n_f=3$ antisymmetric flavours of Dirac fermions in four dimensions. This theory serves as the microscopic origin for composite Higgs models with $SU(4)/Sp(4)$ coset,…
The design of globally $C^s$-smooth ($s \geq 1$) isogeometric spline spaces over multi-patch geometries is a current and challenging topic of research in the framework of isogeometric analysis. In this work, we extend the recent methods…