Related papers: Syzygies of string modules for special biserial al…
We give a complete and explicit description of the kinematical data of higher gauge theory on principal 2-bundles with the string 2-group model of Schommer-Pries as structure 2-group. We start with a self-contained review of the weak…
The aim of this work is to study the ring-theoretic properties of the diagonals of a Rees algebra, which from a geometric point of view are the homogeneous coordinate rings of embeddings of blow-ups of projective varieties along a…
Let $f : X \to S$ be a family of smooth projective algebraic varieties over a smooth connected quasi-projective base $S$, and let $\mathbb{V} = R^{2k} f_{*} \mathbb{Z}(k)$ be the integral variation of Hodge structure coming from degree $2k$…
We provide a classification of generalized tilting modules and full exceptional sequences for the dual extension algebra of the path algebra of a uniformly oriented linear quiver modulo the ideal generated by paths of length two with its…
The stable module category of a selfinjective algebra is triangulated, but need not have any nontrivial $t$-structures, and in particular, full abelian subcategories need not arise as hearts of a $t$-structure. The purpose of this paper is…
In this note we compute length, support and dimension of syzygy modules of certain modules. This partially answers questions asked by Huneke et al.
Homotopy algebra and its involutive generalisation plays an important role in the construction of string field theory. I will review recent progress in these applications of homotopy algebra and its relation to moduli spaces.
We propose an explanation via string theory of the correspondence between the Coulomb branch of certain three-dimensional supersymmetric gauge theories and certain moduli spaces of magnetic monopoles. The same construction also gives an…
We study syzygies of the Segre embedding of P(V_1) x ... x P(V_n), and prove two finiteness results. First, for fixed p but varying n and V_i, there is a finite list of "master p-syzygies" from which all other p-syzygies can be derived by…
Several important cases of vector bundles with extra structure (such as Higgs bundles and triples) may be regarded as examples of twisted representations of a finite quiver in the category of sheaves of modules on a variety/manifold/ringed…
Dualities play a central role in the study of quantum spin chains, providing insight into the structure of quantum phase diagrams and phase transitions. In this work we study categorical dualities, which are defined as bounded-spread…
The goal of this paper and of a subsequent continuation is to find some viable ansatze for the three-loop superstring chiral measure. For this, two alternative formulas are derived for the two-loop superstring chiral measure. Unlike the…
Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods…
In this paper, our primary focus is on investigating the extension dimensions of syzygy module categories associated with Artin algebras, particularly under various equivalences. We demonstrate that, for sufficiently large $i$, the $i$-th…
We relax the definition of a string algebra to also include infinite-dimensional algebras such as k[x,y]/(xy). Using the functorial filtration method, which goes back to Gelfand and Ponomarev, we show that finitely generated and artinian…
Algebra objects in $\infty$-categories of spans admit a description in terms of $2$-Segal objects. We introduce a notion of span between $2$-Segal objects and extend this correspondence to an equivalence of $\infty$-categories.…
A description is given of those sequences ${\Bbb S}= (S(0),S(1),\dots,S(l))$ of simple modules over a finite dimensional algebra for which there are only finitely many uniserial modules with consecutive composition factors…
We study the properties of tilting modules in the context of properly stratified algebras. In particular, we answer the question when the Ringel dual of a properly stratified algebra is properly stratified itself, and show that the class of…
In this paper, we develop the mathematical formulation of metric string structures. These play a crucial role in the formulation of certain six-dimensional superconformal field theories and we believe that they also underlie potential…
We define the notion of adjustment for strict Lie 2-groups and provide the complete cocycle description for non-Abelian gerbes with connections whose structure 2-group is an adjusted 2-group. Most importantly, we depart from the common…