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Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…
Survey article on representation stability and examples in algebraic geometry and topology, written for the Notices of the AMS.
A discussion of homotopy limits of (1-)stacks, with an emphasis on fixed point stacks.
A general upper bound for topological entropy of switched nonlinear systems is constructed, using an asymptotic average of upper limits of the matrix measures of Jacobian matrices of strongly persistent individual modes, weighted by their…
In this paper, for given an algebraic theory $T$ whose category $C$ of models is semi-abelian, we consider the topological models of $T$ called topological $T$-algebras and obtain some results related to the fundamental groups of…
Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other…
We study clustering properties of networks of single integrator nodes over a directed graph, in which the nodes converge to steady-state values. These values define clustering groups of nodes, which depend on interaction topology, edge…
A brief exposition of the point of higher topos theory in (mathematical) physics, commissioned for the Encyclopedia of Mathematical Physics 2nd ed.
Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a…
We produce a large class of hyperbolic homology 3-spheres admitting arbitrarily many distinct tight contact structures. We also produce a sub-class admitting arbitrarily many distinct tight contact structures within the same homotopy class…
Basic concepts and definitions in differential geometry and topology which are important in the theory of solitons and instantons are reviewed. Many examples from soliton theory are discussed briefly, in order to highlight the application…
We study topological group theoretic properties of algebraic groups over local fields. In particular, we find conditions under which such groups have closed images under arbitrary continuous homomorphisms into arbitrary topological groups.
In this paper we will present a way of examining the Stokes structure of certain irregular singular $\mathcal D$-modules, namely the direct image of exponentially twisted regular singular meromorphic connections, in a topological point of…
This survey paper describes the role of splines in geometry and topology, emphasizing both similarities and differences from the classical treatment of splines. The exposition is non-technical and contains many examples, with references to…
This paper surveys some results and methods in topological transformation groups.
A systematic review of the various topologies that can be defined on the projective Hilbert space P(H), i.e., on the set of the pure quantum states, is presented. It is shown that P(H) carries a natural topology as well as a natural…
Possible forms of obstructed atomic limits in quasi-one-dimensional systems are studied using line group symmetry. This is accomplished by revisiting the standard theory with an emphasis on its group-theoretical background, synthesizing the…
In this paper we study the deformation of strictly convex real projective structures on a closed surface. Specially we study the deformation in terms of the entropy on bulging deformations. As a byproduct we construct a sequence of…
We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…