Related papers: Analytic Topology of Groups, Actions, Strings and …
This is an expository article on properties of actions on Lie groups by subgroups of their automorphism groups. After recalling various results on the structure of the automorphism groups, we discuss actions with dense orbits, invariant and…
We introduce a topology on the space of actions modulo weak equivalence finer than the one previously studied in the literature. We show that the product of actions is a continuous operation with respect to this topology, so that the space…
Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…
Some basic notions and results in Topological Dynamics are extended to continuous groupoid actions in topological spaces. We focus mainly on recurrence properties. Besides results that are analogous to the classical case of group actions,…
This article establishes the variational principle of topological pressure for actions of sofic groupoids.
I review few conceptual steps in analytic description of topological interactions, which constitute the basis of a new interdisciplinary branch in mathematical physics, "Statistical Topology", emerged at the edge of topology and statistical…
In this work, we study a class of higher derivative couplings in the string effective action arising at the junction of topological string theory and supersymmetric gauge theories in the $\Omega$-background. They generalise a series of…
In this paper we lay the foundations of an $\infty$-categorical theory of Stokes data.
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Pooling operations have shown to be effective on computer vision and natural language processing tasks. One challenge of performing pooling operations on graph data is the lack of locality that is not well-defined on graphs. Previous…
This article belongs to a subject, Directed Algebraic Topology, whose general aim is including non-reversible processes in the range of topology and algebraic topology. Here, as a further step, we also want to cover "critical processes",…
This paper generalizes sofic entropy theory, in both the topological and measure-theory settings, to actions of locally compact groups. We prove invariance under topological and measure conjugacy of these entropies and establish the…
This paper has been withdrawn by the author. The content of the previous versions is now covered by the more recent papers - math.DG/0610252 (concerning the Lie group structuren on the gauge groups) - math.DG/0612522 (concerning the weak…
A sofic approximation to a countable group is a sequence of partial actions on finite sets that asymptotically approximates the action of the group on itself by left-translations. A group is sofic if it admits a sofic approximation. Sofic…
This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams. It is hoped that this will be useful not just to mathematicians, but also to physicists, computer scientists, and…
The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data…
Various connections between the theory of permutation groups and the theory of topological groups are described. These connections are applied in permutation group theory and in the structure theory of topological groups. The first draft of…
Topological Data Analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data. This includes: clustering, manifold estimation, nonlinear dimension reduction, mode estimation, ridge estimation…
Part I. Some Facts From p-Adic Analysis. Part II. Tables of Integrals.
This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active…