Related papers: Residual regularity in tensor triangular geometry
Random tensor models can be used as combinatorial devices to generate Euclidean dynamical triangulations. A physical continuum limit of dynamical triangulations requires a suitable generalization of the double-scaling limit of random…
This article develops a practical technique for studying representations of $\Bbbk$-linear categories arising in the categorification of quantum groups. We work in terms of locally unital algebras which are $\mathbb{Z}$-graded with graded…
In a triangulated category T with a pair of triangulated subcategories X and Y, one may consider the subcategory of extensions X*Y. We give conditions for X*Y to be triangulated and use them to provide tools for constructing stable…
Different notions on regularity of sets and of collection of sets play an important role in the analysis of the convergence of projection algorithms in nonconvex scenarios. While some projection algorithms can be applied to feasibility…
We constructed some tensor functors that send each exceptional sequence in a module category to another exceptional sequence in another module category by using split extensions and recollements.
In this paper, we characterize several properties of commutative notherian local rings in terms of the left perpendicular category of the category of finitely generated modules of finite projective dimension. As an application we prove that…
We theoretically and experimentally investigate tensor-based regression and classification. Our focus is regularization with various tensor norms, including the overlapped trace norm, the latent trace norm, and the scaled latent trace norm.…
The goal of tensor completion is to fill in missing entries of a partially known tensor under a low-rank constraint. In this paper, we mainly study low rank third-order tensor completion problems by using Riemannian optimization methods on…
These notes are meant to provide a rapid introduction to triangulated categories. We start with the definition of an additive category and end with a glimps of tilting theory. Some exercises are included.
Let C be a finite EI category and k be a field. We consider the category algebra kC. Suppose K(C)=D^b(kC-mod) is the bounded derived category of finitely generated left modules. This is a tensor triangulated category and we compute its…
We establish continuous maximal regularity results for parabolic differential operators acting on sections of tensor bundles on Riemannian manifolds. As an application, we show that solutions to the Yamabe flow instantaneously regularize…
Methods were developed in Ref. [1] for constructing reference metrics (and from them differentiable structures) on three-dimensional manifolds with topologies specified by suitable triangulations. This note generalizes those methods by…
Informed by our understanding of the tt-geometry of permutation modules, we investigate the proper definition of the `stable permutation category' of a finite group. Then we prove that this category decomposes over cyclic and generalized…
We study properties of an array of numbers, called "the triangle," in which each row is formed by rotating all the numbers in the previous row to the left by $m$ positions in cyclical fashion, then appending a number to the end of the row.…
In a general triangulated category, the finiteness of the finitistic dimension serves as a prerequisite for a categorical obstruction, via the singularity category, to the existence of bounded $t$-structures. In this paper, we investigate…
Invariants of generalized tensor fields on a line are classified using special polynomials P_mk^(-1/lambda) introduced here for this purpose. For the case of positive characteristic, a new invariant of formal power series, a width, is…
In this paper, we study metric completions of triangulated categories in a representation-theoretic context. We provide a concrete description of completions of bounded derived categories of hereditary finite dimensional algebras of finite…
We develop the theory of costratification in the setting of relative tensor-triangular geometry, in the sense of Stevenson, providing a unified approach to classification results of Neeman and Benson--Iyengar--Krause, while laying the…
We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic decomposition of higher-order tensors subject to a rank and genericity constraint. Reformulating this computational problem as a system…
Recollements of triangulated categories may be seen as exact sequences of such categories. Iterated recollements of triangulated categories are analogues of geometric or topological stratifications and of composition series of algebraic…