Related papers: Assembly of Constructible Factorization Algebras

A locally conformally product (LCP) structure on a compact conformal manifold is a closed non-exact Weyl connection (i.e.~a linear connection which is locally but not globally the Levi-Civita connection of Riemannian metrics in the…

Working over an algebraically closed field $k$ of any characteristic, we determine the matrix factorizations for the --- suitably graded --- triangle singularities $f=x^a+y^b+z^c$ of domestic type, that is, we assume that $(a,b,c)$ are…

We start from any small strict monoidal braided Ab-category and extend it to a monoidal nonstrict braided Ab-category which contains braided bialgebras. The objects of the original category turn out to be modules for these bialgebras

Factorization algebras have been defined using three different topologies on the Ran space. We study these three different topologies on the exponential, which is the union of the Ran space and the empty configuration, and show that an…

Using an existence criterion for good moduli spaces of Artin stacks by Alper-Fedorchuk-Smyth we construct a proper moduli space of rank two sheaves with fixed Chern classes on a given complex projective manifold that are…

Factorization structures occur in toric differential and discrete geometry, and can be viewed in multiple ways, e.g., as objects determining substantial classes of explicit toric Sasaki and K\"ahler geometries, as special coordinates on…

Any cluster-tilted algebra is the relation extension of a tilted algebra. We present a method to, given the distribution of a cluster-tilting object in the Auslander-Reiten quiver of the cluster category, construct all tilted algebras whose…

To any directed graph we associate an algebra with edges of the graph as generators and with relations defined by all pairs of directed paths with the same origin and terminus. Such algebras are related to factorizations of polynomials over…

We introduce a class of algebras over a field $\mathbb{F}$ related to directed graphs in which all edges are labeled by nonzero elements of the field $\mathbb{F}$. If all labels are different from $1$, these algebras are axial algebras. We…

We present a categorification of four mutation finite cluster algebras by the cluster category of the category of coherent sheaves over a weighted projective line of tubular weight type. Each of these cluster algebras which we call tubular…

We propose a sequential topology on the space of sub-$\sigma$-algebras of a separable probability space $(\Omega,\mathcal{F},\mathbb{P})$ by linking conditional expectations on $L^{2}$ along sequences of sub-$\sigma$-algebras. The varying…

Given a stratified variety X with strata satisfying a cohomological parity-vanishing condition, we define and show the uniqueness of "parity sheaves", which are objects in the constructible derived category of sheaves with coefficients in…

In this short note we present a generating function computing the compactly supported Euler characteristic $\chi_c(F(X, n), K^{\boxtimes n})$ of the configuration spaces on a topologically stratified space $X$, with $K$ a constructible…

Using the wonderful compactification of a semisimple adjoint affine algebraic group G defined over an algebraically closed field k of arbitrary characteristic, we construct a natural compactification Y of the G-character variety of any…

Given a stratified topological space, we answer the question whether the functor from the derived category of constructible sheaves to the derived category of sheaves with constructible cohomology is an equivalence. We also establish basic…

Let $A$ be a Banach algebra with a bounded left approximate identity $\{e_\lambda\}_{\lambda\in\Lambda}$, let $\pi$ be a continuous representation of $A$ on a Banach space $X$, and let $S$ be a non-empty subset of $X$ such that…

We study local normal forms for completely integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The existence of Weinstein's…

Let $X$ be a variety over a finite field. Given an order $R$ in a semi-simple algebra over the rationals and a constructible \'etale sheaf $F$ of $R$-modules over $X$, one can consider a natural non-commutative $L$-function associated with…

The aim of this note is threefold. The first is to obtain a simple characterization of relative constructible sheaves when the parameter space is projective. The second is to study the relative Fourier-Mukai for relative constructible…

We construct a compact closed category out of any symmetric monoidal category by freely adding adjoints to its objects. The morphisms of the completion are defined as string diagrams annotated by objects and morphisms from the original…