Related papers: Singularity categories of locally bounded categori…
We study rational double points over algebraically closed fields in arbitrary characteristics and completely classify the indecomposable objects in their singularity categories, which correspond to the vertices in their Auslander-Reiten…
In this paper we consider categories over a commutative ring provided either with a free action or with a grading of a not necessarily finite group. We define the smash product category and the skew category and we show that these…
We will briefly review the definition and classification of classical and quantum singularities in general relativity. Examples of classically singular spacetimes that do not have quantum singularities will be given. We will present results…
We study locally finitary realizations of simple transitive module categories of infinite rank over the monoidal category $\mathscr{C}$ of finite dimensional modules for the complex Lie algebra $\mathfrak{sl}_2$. Combinatorics of such…
We study the categories of singularities coming from Landau-Ginzburg models given by the invertible polynomials. Such categories appear on the B-side of the Berglund-H\"ubsch mirror symmetry. We provide an efficient method of computing…
We prove that over an algebraically closed field of characteristic not two the problems of classifying pairs of sesquilinear forms in which the second is Hermitian, pairs of bilinear forms in which the second is symmetric (skew-symmetric),…
This work is an attempt towards a Morita theory for stable equivalences between self-injective algebras. More precisely, given two self-injective algebras A and B and an equivalence between their stable categories, consider the set S of…
We study the local symplectic algebra of the 1-dimensional isolated complete intersection singularity of type S{\mu}. We use the method of algebraic restrictions to classify symplectic S{\mu} singularities. We distinguish these symplectic…
We establish a Morita theorem to construct triangle equivalences between the singularity categories of (commutative and non-commutative) Gorenstein rings and the cluster categories of finite dimensional algebras over fields, and more…
For a $p$-adic field $F$ of residual cardinality $q$, we provide a triangulated equivalence between the bounded derived category $D^b(\mathcal{B}_{1}(G)_{fg})$ of finitely generated unipotent representations of $G=\mathrm{GL}_2(F)$ and…
We determine explicitly the irreducible components of the singular locus of any Schubert variety for GL_n(K), K being an algebraically closed field of arbitrary characteristic. We also describe the generic singularities along these…
Let X be a proper CAT(0) space. A halfspace system (or cubulation) of X is a set H of open halfspaces closed under closure-complementation and such that every point in X has a neighbourhood intersecting only finitely many walls of H. Given…
Given an essentially small triangulated category it is possible to give a metric on it, to complete it with respect to the metric, and to look at the subcategory of objects in the completion which are compactly supported with respect to the…
We give a detailed proof of the following fundamental result: the singularity category of a ring is triangle equivalent to the stabilization of its stable module category. The result yields singular equivalences between rings of different…
In this thesis we define the notion of a locally stratified space. Locally stratified spaces are particular kinds of streams and d-spaces which are locally modelled on stratified spaces. We construct a locally presentable and cartesian…
The main result here gives an algebra(/linear category) isomorphism between a geometrically defined subcategory $J^1_0$ of a short Brauer category $J_0$ and a certain one-parameter specialisation of the blob category $b$. That is, we prove…
Take a bounded symmetric domain $D$ and an arithmetic subgroup $\Gamma$ of ${\rm Aut}(D)$. Take the quotient $D/\Gamma$, compactify and resolve the singularities. We study the fundamental group of the compact complex manifolds that result…
The unitary representation theory of locally compact contraction groups and their semi-direct products with $\mathbb{Z}$ is studied. We put forward the problem of completely characterising such groups which are type I or CCR and this…
We extend the scope of Balmer's tensor triangular Chow groups to compactly generated triangulated categories $\mathcal{K}$ that only admit an action by a compactly-rigidly generated tensor triangulated category $\mathcal{T}$ as opposed to…
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.…