Related papers: Weight filtrations on GKZ-systems

Let $G$ be a complex reductive group, $\theta \colon G \to G$ an involution, and $K = G^\theta$. In arXiv:1206.5547, W. Schmid and the second named author proposed a program to study unitary representations of the corresponding real form…

We show the existence of "Zagier duality" between vector valued harmonic weak Maass forms and vector valued weakly holomorphic modular forms of integral weight. This duality phenomenon arises naturally in the context of harmonic weak Maass…

This paper is dedicated to the study of weight complexes (defined on triangulated categories endowed with weight structures) and their applications. We introduce pure (co)homological functors that "ignore all non-zero weights"; these have a…

Heavy fermion systems, traditionally realized in rare-earth compounds with limited tunability, have hindered systematic exploration of correlated quantum phenomena. Here, we introduce a general strategy for engineering heavy fermions in…

We show that the dualizing sheaves of reduced simple normal crossings pairs have a canonical weight filtration in a compatible way with the one on the corresponding mixed Hodge modules by calculating the extension classes between the…

In this paper we formulate a conjecture which partially generalizes the Gross-Kohnen-Zagier theorem to higher weight modular forms. For f in S_k(N) satisfying certain conditions, we construct a map from the Heegner points of level N to a…

We study affine cartesian codes, which are a Reed-Muller type of evaluation codes, where polynomials are evaluated at the cartesian product of n subsets of a finite field F_q. These codes appeared recently in a work by H. Lopez, C.…

Let $\mathbb{V}$ be an admissible and graded-polarized integral variation of mixed Hodge structures over a smooth and irreducible complex algebraic variety $S$. We show that if the typical Hodge locus…

In this paper, as the first step towards classification of simple weight modules with finite dimensional weight spaces over Witt algebras $W_n$, we explicitly describe supports of such modules. We also obtain some descriptions on the…

Using principal series Harish-Chandra modules, local cohomology with support in Schubert cells and twisting functors we construct certain modules parametrized by the Weyl group and a highest weight in the subcategory O of the category of…

The geometric description of open quantum systems via the Quantum Geometric Tensor (QGT) traditionally relies on the assumption that the physical states form a differentiable vector bundle over the parameter manifold. This framework becomes…

Gravitational-wave data is gauge dependent. While we can restrict the class of gauges in which such data may be expressed, there will still be an infinite-dimensional group of transformations allowed while remaining in this class, and…

In order to cluster or partition data, we often use Expectation-and-Maximization (EM) or Variational approximation with a Gaussian Mixture Model (GMM), which is a parametric probability density function represented as a weighted sum of…

String compactification with fluxes yields MSSM soft SUSY breaking terms that receive comparable contributions from modulus and anomaly mediation whose relative strength is governed by a phenomenological parameter $\alpha$. Gaugino and…

Type-A toric varieties may be obtained as GIT quotients with respect to a torus action with weights corresponding to roots of the group $SL(k)$ for some $k>1$. These varieties appear in various important applications, in particular, as…

We review mirror symmetry for the quantum cohomology D-module of a compact weak-Fano toric manifold. We also discuss the relationship to the GKZ system, the Stanley-Reisner ring, the Mellin-Barnes integrals, and the Gamma-integral…

We construct the limiting mixed Hodge structure of a degeneration of compact K\"ahler manifolds over the unit disk with a possibly non-reduced simple normal crossing singular central fiber via holonomic $\mathscr D$-modules, generalizing…

Let X be a smooth, projective variety over the field of complex numbers. On the space H of its rational cohomology of degree i we have the arithmetic filtration F^p. On the other hand, on the space of cohomology of degree i of X with…

The theory of gravitational wave turbulence describes the long-term statistical behaviour of a set of weakly nonlinear interacting waves. In this paper, we aim to study aspects of gravitational turbulence within the framework of general…

Let G be a complex reductive algebraic group. We study complete intersections in a spherical homogeneous space G/H defined by a generic collection of sections from G-invariant linear systems. Whenever nonempty, all such complete…