Related papers: High dimensional expanders and coset geometries
We prove that the derived categories of abelian categories have unique enhancements -- all of them, the unbounded, bounded, bounded above and bounded below derived categories. The unseparated and left completed derived categories of a…
Higher order networks are able to characterize data as different as functional brain networks, protein interaction networks and social networks beyond the framework of pairwise interactions. Most notably higher order networks include…
Design matrices are sparse matrices in which the supports of different columns intersect in a few positions. Such matrices come up naturally when studying problems involving point sets with many collinear triples. In this work we consider…
A problem of recent interest has been to study how large subsets of the natural numbers can be while avoiding 3-term geometric progressions. Building on recent progress on this problem, we consider the analogous problem over quadratic…
A right-angled Coxeter group is a group with a given set of generators of order two, subject only to the relations that certain pairs of the generators commute. Various papers have shown how homological properties of the Coxeter group are…
We introduce shortcut graphs and groups. Shortcut graphs are graphs in which cycles cannot embed without metric distortion. Shortcut groups are groups which act properly and cocompactly on shortcut graphs. These notions unify a surprisingly…
The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…
We introduce group crosscoders, an extension of crosscoders that systematically discover and analyse symmetrical features in neural networks. While neural networks often develop equivariant representations without explicit architectural…
We apply the homomorphism complex construction to partially ordered sets, introducing a new topological construction based on the set of maximal chains in a graded poset. Our primary objects of study are distributive lattices, with special…
We develop a new approach for approximating large independent sets when the input graph is a one-sided spectral expander - that is, the uniform random walk matrix of the graph has its second eigenvalue bounded away from 1. Consequently, we…
We introduce the notion of \emph{topo-symmetric extensions} of topological groups, a new generalization of classical group extensions that incorporates both topological and symmetry constraints. We define morphisms between such extensions,…
Many models of fractal growth patterns (like Diffusion Limited Aggregation and Dielectric Breakdown Models) combine complex geometry with randomness; this double difficulty is a stumbling block to their elucidation. In this paper we…
In this paper we provide a framework for the study of isoperimetric problems in finitely generated group, through a combinatorial study of universal covers of compact simplicial complexes. We show that, when estimating filling functions,…
Graphs, and sequences of growing graphs, can be used to specify the architecture of mathematical models in many fields including machine learning and computational science. Here we define structured graph "lineages" (ordered by level…
We introduce graphical complexes of groups, which can be thought of as a generalisation of Coxeter systems with 1-dimensional nerves. We show that these complexes are strictly developable, and we equip the resulting Basic Construction with…
The aim of this work is to develop a systematic manner to close overdetermined systems arising from conformal Killing tensors (CKT). The research performs this action for 1-tensor and 2-tensors. This research makes it possible to develop a…
We characterise the quotient surface graphs arising from symmetric contact systems of line segments in the plane and also from symmetric pointed pseudotriangulations in the case where the group of symmetries is generated by a translation or…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
Double triangle expansion is an operation on $4$-regular graphs with at least one triangle which replaces a triangle with two triangles in a particular way. We study the class of graphs which can be obtained by repeated double triangle…
This write-up contains some minor results and notes related to our work [HQ15] (some of them already known in the literature). In particular, it shows the following: - We show that a graph with polynomial expansion have sublinear…