Related papers: SPM Bulletin 38
These lecture notes attempt to invite the reader towards the theory of singular foliations, both smooth and holomorphic. In addition to a systematic review of the foundations, and an attempt to put in order examples and several elementary…
Short survey to be published at the Encyclopedia of Mathematical Physics.
This paper explains unexpected links between the 3 topics in the title and frames them in a large canvas.
Topological phases of matter are ubiquitous in crystals, but less is known about their existence in amorphous systems, that lack long-range order. In this perspective, we review the recent progress made on theoretically defining amorphous…
Feature requests are proposed by users to request new features or enhancements of existing features of software products, which represent users' wishes and demands. Satisfying users' demands can benefit the product from both competitiveness…
A compendium of thirty previously published open problems in computational geometry is presented.
In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…
The main purpose of this paper is to give a topological and symplectic classification of completely integrable Hamiltonian systems in terms of characteristic classes and other local and global invariants.
The number of researchers, articles, journals, conferences, funding opportunities, and other such scholarly resources continues to grow every year and at an increasing rate. Many services have emerged to support scholars in navigating…
Stable fold maps are fundamental tools in a generalization of the theory of Morse functions on smooth manifolds and its application to studies of geometric properties of smooth manifolds. Round fold maps were introduced as stable fold maps…
In this note, we investigate some topological properties of probabilistic modular spaces.
The THedu'11 workshop received thirteen submissions, twelve of which were accepted and presented during the workshop. For the post-conference proceedings nine submission where received and accepted. The submissions are within the scope of…
In this paper I suggest an alternative approach (using generic flat bundles and higher Massey products) to a Lusternik-Schnirelman type theory for closed 1-forms (cf. also math.DG/9811113)
Recent years have seen a growing interest in topological phases beyond the standard paradigm of gapped, isolated systems. One recent direction is to explore topological features in non-hermitian systems that are commonly used as effective…
Table of contents: Editorial 1 Correspondents 3 Some recent work in general relativistic Astrophysics 4 Two dimensional black holes 6 Resonant-mass gravitational wave detectors: an update 8 Universality and scaling in gravitational collapse…
Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and…
These informal notes deal with a number of questions related to sums and integrals in analysis.
Issues relevant to the flow chirality and structure are focused, while the new theoretical results, including even a distinctive theory, are introduced. However, it is hope that the presentation, with a low starting point but a steep rise,…
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.
Quantum graphs have become in this century a favorite playground for mathematicians, mathematical physicists, and chemists, due to their manifold applications as models of thin structures, as well as presenting sometimes simpler playground…