Related papers: A note on gamma triangles and local gamma vectors
The present paper is devoted to clustering geometric graphs. While the standard spectral clustering is often not effective for geometric graphs, we present an effective generalization, which we call higher-order spectral clustering. It…
For any essentially small triangulated category the centre of its lattice of thick subcategories is introduced; it is a spatial frame and yields a notion of central support. A relative version of this centre recovers the support theory for…
Let $K$ be a field, $\Gamma $ a finite group of field automorphisms of $K$, $F$ the $\Gamma $-fixed field in $K$ and $G\leq $GL$_v(K)$ a finite matrix group. Then the action of $\Gamma $ defines a grading on the symmetric algebra of the…
We derive an efficient method to perform clustering of nodes in Gaussian graphical models directly from sample data. Nodes are clustered based on the similarity of their network neighborhoods, with edge weights defined by partial…
We give a systematic construction of semiorthogonal decompositions of derived categories of coherent sheaves on quasi-smooth derived algebraic stacks over $\mathbb{C}$, where the summands are subcategories defined by weight conditions, and…
This expository article presents a self-contained introduction to simplicial homology for finite simplicial complexes, emphasizing concrete computation and geometric intuition. Beginning with orientations of simplices and the construction…
Associated with some finite dimensional algebras of global dimension at most 2, a generalized cluster category was introduced in \cite{Ami3}, which was shown to be triangulated and 2-Calabi-Yau when it is $\Hom$-finite. By definition, the…
The Hamiltonian dynamics of spherically symmetric massive thin shells in the general relativity is studied. Two different constraint dynamical systems representing this dynamics have been described recently; the relation of these two…
We collect three observations on the homology for Smale spaces defined by Putnam. The definition of such homology groups involves four complexes. It is shown here that a simple convergence theorem for spectral sequences can be used to prove…
This paper explores the cluster algebra structure of the moduli space $\mathscr{A}_{\mathrm{SL}_{n+1},\mathbb{S}}$ of twisted $\mathrm{SL}_{n+1}$-local systems on a surface. We derive general recurrence relations for cluster variables…
A rigorous connection between large deviations theory and Gamma-convergence is established. Applications include representations formulas for rate functions, a contraction principle for measurable maps, a large deviations principle for…
This note revisits localisation and patching method in the setting of generalised unitary groups. Introducing certain subgroups of relative elementary unitary groups, we develop relative versions of the conjugation calculus and the…
R. Stanley has found a nice combinatorial formula for characters of irreducible representations of the symmetric group of rectangular shape. Then, he has given a conjectural generalisation for any shape. Here, we will prove this formula…
The morphology of galaxy clusters is quantified using Minkowski functionals, especially the vector-valued ones, which contain directional information and are related to curvature centroids. The asymmetry of clusters and the amount of their…
We introduce the notion of homological systems $\Theta$ for triangulated categories. Homological systems generalize, on one hand, the notion of stratifying systems in module categories, and on the other hand, the notion of exceptional…
The paper surveys some recent results concerning vector analysis on fractals. We start with a local regular Dirichlet form and use the framework of 1-forms and derivations introduced by Cipriani and Sauvageot to set up some elements of a…
Let $K$ be a finite extension of $\mathbb{Q}_{p}$ and let $\Gamma$ be the Galois group of the cyclotomic extension of $K$. Fontaine's theory gives a classification of $p$-adic representations of $\mathrm{Gal}\left(\overline{K}/K\right)$ in…
Let $G$ be a commutative algebraic group embedded in projective space and $\Gamma$ a finitely generated subgroup of $G$. From these data we construct a chain of algebraic subgroups of $G$ which is intimately related to obstructions to…
To a pair $(A,s)$ consisting of a smooth, cyclic $A_\infty$-algebra $A$ and a splitting $s$ of the Hodge filtration on its Hochschild homology Costello (2005) associates an invariant which conjecturally generalizes the total descendant…
One can explicitly compute the generators of a surface cluster algebra either combinatorially, through dimer covers of snake graphs, or homologically, through the CC-map applied to indecomposable modules over the appropriate algebra. Recent…