Related papers: Tensor triangular geometry of filtered objects and…
For an arbitrary $\infty$-topos, we classify the smashing localizations in the $\infty$-category of sheaves valued in derived vector spaces: Any of them is the restriction functor to a (unique) closed subtopos. Our proof is based on the…
We develop a valuation-theoretic framework for studying tangent cones of torsion-free sheaves on algebraic varieties. To analyze these objects, we introduce a slope stability theory, including the Harder-Narasimhan filtrations, for finitely…
We prove new Brown representability theorems for triangulated categories using metric techniques as introduced in the work of Neeman. In the setting of algebraic geometry, this gives us new representability theorems for homological and…
Dimer models (also known as brane tilings) are special bipartite graphs on a torus $\mathbb{T}^2$. They encode the structure of the 4d $\mathcal{N} = 1$ worldvolume theories of D3 branes probing toric affine Calabi-Yau singularities.…
One of the apparent advantages of quantum computers over their classical counterparts is their ability to efficiently contract tensor networks. In this article, we study some implications of this fact in the case of topological tensor…
We compute the Balmer spectrum of the category of perfect complexes on an algebraic stack admitting a finite locally free cover by an affine scheme and identify it with the homogeneous spectrum of the cohomology ring.
Consider a data set collected by (individuals-features) pairs in different times. It can be represented as a tensor of three dimensions (Individuals, features and times). The tensor biclustering problem computes a subset of individuals and…
We initiate a systematic study of lattices of thick subcategories for arbitrary essentially small triangulated categories. To this end we give several examples illustrating the various properties these lattices may, or may not, have and…
In a recent collaboration, Hiroki Matsui and the author introduced a new proof of the reconstruction theorem of Bondal-Orlov and Ballard, using Matsui's construction of a ringed space associated to a triangulated category. This paper first…
We introduce and study the definition, main properties and applications of iterated twisted tensor products of algebras, motivated by the problem of defining a suitable representative for the product of spaces in noncommutative geometry. We…
We present a new class of efficient and robust discontinuous spectral-element methods of arbitrary order for nonlinear hyperbolic systems of conservation laws on curved triangular and tetrahedral unstructured grids. Such discretizations…
We study linear problems defined on tensor products of Hilbert spaces with an additional (anti-) symmetry property. We construct a linear algorithm that uses finitely many continuous linear functionals and show an explicit formula for its…
This article provides an overview of the techniques related to classification of spherical and more general objects within triangulated categories, and its relationship with algebraic geometry, representation theory and symplectic geometry.…
We solve tensor balancing, rescaling an Nth order nonnegative tensor by multiplying N tensors of order N - 1 so that every fiber sums to one. This generalizes a fundamental process of matrix balancing used to compare matrices in a wide…
We investigate invertible elements and gradings in braided tensor categories. This leads us to the definition of theta-, product-, subgrading and orbitcategories in order to construct new families of BTC's from given ones. We use the…
We develop and analyze iterative methods for computing the principal square root of third-order tensors under the T-product framework. Tensor extensions of the Newton iteration (quadratic convergence) and the Denman--Beavers iteration…
We describe the Tate resolution of a coherent sheaf or complex of coherent sheaves on a product of projective spaces. Such a resolution makes explicit all the cohomology of all twists of the sheaf, including, for example, the multigraded…
We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
Most of the existing works use projection functions for ternary quantization in discrete space. Scaling factors and thresholds are used in some cases to improve the model accuracy. However, the gradients used for optimization are inaccurate…