Related papers: Harder-Narasimhan Filtrations of Persistence Modul…

Suppose V is a finite dimensional, complex vector space, A is a finite set of codimension one subspaces of V, and G is a finite subgroup of the general linear group GL(V) that permutes the hyperplanes in A. In this paper we study invariants…

We investigate a one-parameter family of quantum Harish-Chandra modules of U_q sl(2n). This family is an analog of the holomorphic discrete series of representations of the group SU(n,n) for the quantum group U_q su(n, n). We introduce a…

We show that the bases of irreducible integrable highest weight module of a non-symmetric Kac-Moody algebra, which is associated to a quiver with a nontrivial admissible automorphism, can be naturally identified with a set of certain…

We prove that pointwise finite-dimensional S^1 persistence modules over an arbitrary field decompose uniquely, up to isomorphism, into the direct sum of a bar code and finitely-many Jordan cells. These persistence modules have also been…

Support matrix machine (SMM) is an emerging classification framework that directly handles matrix-structured observations, thereby avoiding the spatial correlations destroyed by vectorization. However, most existing SMM variants rely on…

We introduce a new class of representations of the cohomological Hall algebras of Kontsevich and Soibelman, which we call cohomological Hall modules, or CoHM for short. These representations are constructed from self-dual representations of…

Commutative diagrams of vector spaces and linear maps over $\mathbb{Z}^2$ are objects of interest in topological data analysis (TDA) where this type of diagrams are called 2-parameter persistence modules. Given that quiver representation…

Multidimensional persistence has been proposed to study the persistence of topological features in data indexed by multiple parameters. In this work, we further explore its algebraic complications from the point of view of higher…

We study Maurer-Cartan moduli spaces of dg algebras and associated dg categories and show that, while not quasi-isomorphism invariants, they are invariants of strong homotopy type, a natural notion that has not been studied before. We…

Motivated by S-duality modularity conjectures in string theory, we study the Donaldson-Thomas type invariants of pure 2-dimensional sheaves inside a nonsingular threefold X in three different situations: (1). X is a K3 fibration over a…

In this article we study the principal block of the category of real Harish-Chandra modules for the group $\mathsf{SL}_2(\RR)$ and relate it to the category of finite dimensional modules over the so-called real Gelfand order. We describe…

This paper is devoted to the full system of incompressible liquid crystals, as modeled in the Q-tensor framework. The main purpose is to establish the uniqueness of weak solutions in a two dimensional setting, without imposing an extra…

Suppose that $\mathcal{E}$ is a vector bundle on a smooth projective variety $X$. Given a family of curves $C$ on $X$, we study how the Harder-Narasimhan filtration of $\mathcal{E}|_{C}$ changes as we vary $C$ in our family. Heuristically…

Multiparameter persistence is a natural extension of the well-known persistent homology, which has attracted a lot of interest. However, there are major theoretical obstacles preventing the full development of this promising theory. In this…

We consider the Harder-Narasimhan formalism on the category of normed isocrystals and show that the Harder-Narasimhan filtration is compatible with tensor products which generalizes a result of Cornut. As an application of this result, we…

Let $H$ be a hereditary artin algebra of finite representation type. We first determine all hammocks in the Auslander-Reiten quiver $\GaH$ of $\mmod H$, the category of finitely generated left $H$-modules. This enables us to obtain an…

We compute the number of finite dimensional irreducible modules for the algebras quantizing Nakajima quiver varieties. We get a lower bound for all quivers and vectors of framing and provide an exact count in the case when the quiver is of…

We show that the Hodge numbers of Sasakian manifolds are invariant under arbitrary deformations of the Sasakian structure. We also present an upper semi continuity Theorem for the dimensions of kernels of a smooth family of transversely…

Persistent homology was shown by Carlsson and Zomorodian to be homology of graded chain complexes with coefficients in the graded ring $\kk[t]$. As such, the behavior of persistence modules -- graded modules over $\kk[t]$ is an important…

Given an infinite reductive algebraic group $G$, we consider $G$-equivariant coherent sheaves with prescribed multiplicities, called $(G,h)$-constellations, for which two stability notions arise. The first one is analogous to the…