Related papers: Syzygies of string modules for special biserial al…
We aim at modelling the appearance of distinct tags in a sequence of labelled objects. Common examples of this type of data include words in a corpus or distinct species in a sample. These sequential discoveries are often summarised via…
In this article we study in detail the category of noncommutative motives of separable algebras Sep(k) over a base field k. We start by constructing four different models of the full subcategory of commutative separable algebras CSep(k).…
We survey results on multiserial algebras, special multiserial algebras and Brauer configuration algebras. A structural property of modules over a special multiserial algebra is presented. Almost gentle algebras are introduced and we…
A Bialgebra is a module over a ring that is both an associative algebra and a co-associative coalgebra with the product and coproduct additionally satisfying an appropriate commutative relationship. One application of Bialgebras is in the…
It has recently been observed that IIB string theory in the pp-wave background can be used to calculate certain quantities, such as the dimensions of BMN operators, as exact functions of the effective coupling lambda' = lambda/J^2. These…
We lay the foundations for a general approach to nonassociative spectral geometry as an extension of Connes' noncommutative geometry by explaining how to construct finite-dimensional, discrete spectral geometries with exceptional symmetry,…
We provide the first explicit example of Type IIB string theory compactification on a globally defined Calabi-Yau threefold with torsion which results in a four-dimensional effective theory with a non-Abelian discrete gauge symmetry. Our…
The paper presents a detailed description of duality for braided algebras, coalgebras, bialgebras, Hopf algebras and their modules and comodules in the infinite setting. Assuming that the dual objects exist, it is shown how a given braiding…
Four-dimensional compactifications of string theory provide a controlled set of possible gauge representations accounting for BSM particles and dark sector components. In this review, constraints from perturbative Type II string…
We apply the theory of Groebner bases to the computation of free resolutions over a polynomial ring, the defining equations of a canonically embedded curve, and the unirationality of the moduli space of curves of a fixed genus.
We consider the problem of Bayesian inference in the family of probabilistic models implicitly defined by stochastic generative models of data. In scientific fields ranging from population biology to cosmology, low-level mechanistic…
As an example of the categorical apparatus of pseudo algebras over 2-theories, we show that pseudo algebras over the 2-theory of categories can be viewed as pseudo double categories with folding or as appropriate 2-functors into…
We review diverse two-dimensional models emerging on the world sheet of non-Abelian strings in the low-energy limit. Non-Abelian strings are supported in a class of four-dimensional bulk theories with or without supersymmetry. In…
B-series and generalizations are a powerful tool for the analysis of numerical integrators. An extension named exotic aromatic B-series was introduced to study the order conditions for sampling the invariant measure of ergodic SDEs.…
In this work, we introduce Regularity Structures B-series which are used for describing solutions of singular stochastic partial differential equations (SPDEs). We define composition and substitutions of these B-series and as in the context…
Sigma models on semi-symmetric spaces provide the central building block for string theories on AdS backgrounds. Under certain conditions on the global supersymmetry group they can be made one-loop conformal by adding an appropriate…
I summarize and discuss some recent results on formulating actions of six-dimensional superconformal field theories using the language of higher gauge theory. The latter guarantees mathematical consistency of our constructions and we review…
We develop a semistability algorithm for vector bundles which are given as a kernel of a surjective morphism between splitting bundles on the projective space over an algebraically closed field K. This class of bundles is a generalization…
We prove that among the finite dimensional algebras of finite representation type those that are string algebras are precisely the ones that have the property that the middle term of an arbitrary extension of indecomposable modules has at…
The gauge symmetries that underlie string theory arise from inner automorphisms of the algebra of observables of the associated conformal field theory. In this way it is possible to study broken and unbroken symmetries on the same footing,…