Related papers: An optimal representation for the trace zero subgr…

We produce a sequence of finite dimensional representations of the fundamental group $\pi_1(S)$ of a closed surface where all simple closed curves act with finite order, but where each non--simple closed curve eventually acts with infinite…

We introduce a decomposition method for the distributed calculation of exact Euclidean Minimum Spanning Trees in high dimensions (where sub-quadratic algorithms are not effective), or more generalized geometric-minimum spanning trees of…

The multidimensional quantization procedure, proposed by the first author and its modifications (reduction to radicals and lifting on U(1)-coverings) give us a almost universal theoretical tools to find irreducible representations of Lie…

Hierarchical graph clustering is a common technique to reveal the multi-scale structure of complex networks. We propose a novel metric for assessing the quality of a hierarchical clustering. This metric reflects the ability to reconstruct…

This is a survey paper about representation theory and noncommutative geometry of reductive p-adic groups G. The main focus points are: 1. The structure of the Hecke algebra H(G), the Harish-Chandra-Schwartz algebra S(G) and the reduced…

We consider exact sequences and lower central series of surface braid groups and we explain how they can prove to be useful for obtaining representations for surface braid groups. In particular, using a completely algebraic framework, we…

We prove that finitely generated higher dimensional Kleinian groups with small critical exponent are always convex-cocompact. Along the way, we also prove some geometric properties for any complete pinched negatively curved manifold with…

The paper is devoted to a study of the cone $\cop$ of copositive matrices. Based on the known from semi-infinite optimization concept of immobile indices, we define zero and minimal zero vectors of a subset of the cone $\cop$ and use them…

Algebra and representation theory in modular tensor categories can be combined with tools from topological field theory to obtain a deeper understanding of rational conformal field theories in two dimensions: It allows us to establish the…

We investigate group coding for arbitrary finite groups acting linearly on a vector space. These yield robust codes based on real or complex matrix groups. We give necessary and sufficient conditions for correct subgroup decoding using…

We address the problem of computing in the group of $\ell^k$-torsion rational points of the jacobian variety of algebraic curves over finite fields, with a view toward computing modular representations.

Let G be the group of rational points of a connected reductive group over a finite field. Based on work of Lusztig and Yun, we make the Jordan decomposition for irreducible G-representations canonical. It comes in the form of an equivalence…

Exponential integrators based on contour integral representations lead to powerful numerical solvers for a variety of ODEs, PDEs, and other time-evolution equations. They are embarrassingly parallelizable and lead to global-in-time…

Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…

Let G be a connected reductive group over a field of characteristic zero, and consider an orthogonal representation of G. We give a simple criterion for whether the representation lifts to the spin group, in terms of the highest weights of…

We present a succinct data structure for permutation graphs, and their superclass of circular permutation graphs, i.e., data structures using optimal space up to lower order terms. Unlike concurrent work on circle graphs (Acan et al. 2022),…

Semidefinite Programming (SDP) provides tight lower bounds for Optimal Power Flow problems. However, solving large-scale SDP problems requires exploiting sparsity. In this paper, we experiment several clique decomposition algorithms that…

This paper presents a method to build explicit tensor-train (TT) representations. We show that a wide class of tensors can be explicitly represented with sparse TT-cores, obtaining, in many cases, optimal TT-ranks. Numerical experiments…

Two fundamental ways to represent a group are as permutations and as matrices. In this paper, we study linear representations of groups that intertwine with a permutation representation. Recently, D'Alconzo and Di Scala investigated how…

We study isometric representations of the semigroup $\mathbb{Z}_+\backslash \{1\}$. Notion of an inverse representation is introduced and a complete description (up to unitary equivalence) of such representations is given. Also, we study a…