Related papers: Holonomic Systems for Period Mappings

Answering all questions---concerning proper holomorphic mappings between generalized Hartogs triangles---posed by Jarnicki and Plfug (First steps in several complex variables: Reinhardt domains, 2008) we characterize the existence of proper…

The topology of periodic spaces has attracted a lot of interest in recent years in order to study and classify crystalline structures and other large homogeneous data sets, such as the distribution of galaxies in cosmology. In practice,…

The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…

Periodic and semi periodic patterns are very common in nature. In this paper we introduce a topological toolbox aiming in detecting and quantifying periodicity. The presented technique is of a general nature and may be employed wherever…

A variation of Hodge structure is a horizontal holomorphic mapping into a flag domain D; here "horizontal" indicates that the image of the map satisfies a system of partial differential equations known as the infinitesimal period relation…

A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is a central tool in topological data analysis, which examines…

This survey article is the outgrowth of two talks given at the Journ\'ees X-UPS "P\'eriodes et transcendance" at \'Ecole polytechnique. Periods are complex numbers whose real and imaginary parts can be written as integrals of rational…

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…

For more than 150 years the structure of the periodic system of the chemical elements has intensively motivated research in different areas of chemistry and physics. However, there is still no unified picture of what a periodic system is.…

The purpose of this article is to show a second main theorem with the explicit truncation level for holomorphic mappings of $ \mathbb{C} $ (or of a compact Riemann surface) into a compact complex manifold sharing divisors in subgeneral…

We give practical numerical methods to compute the period matrix of a plane algebraic curve (not necessarily smooth). We show how automorphisms and isomorphisms of such curves, as well as the decomposition of their Jacobians up to isogeny,…

Although topological band theory has been used to discover and classify a wide array of novel topological phases in insulating and semi-metal systems, it is not well-suited to identifying topological phenomena in metallic or gapless…

We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is…

The study of spatial symmetries was accomplished during the last century, and had greatly improved our understanding of the properties of solids. Nowadays, the symmetry data of any crystal can be readily extracted from standard…

The modern conception of phases of matter has undergone tremendous developments since the first observation of topologically ordered states in fractional quantum Hall systems in the 1980s. In this paper, we explore the question: How much…

In order to make the fundamental group, one of the most well known invariants in algebraic topology, more useful and powerful some researchers have introduced and studied various topologies on the fundamental group from the beginning of the…

In previous work it had been shown that the remarkable homogeneous space $M= \operatorname{Diff}(S^1)/\operatorname{PSL} (2,\Bbb{R})$ sits as a complex analytic and K\"ahler submanifold of the Universal Teichm\"uller Space. There is a…

Recurrence is a fundamental characteristic of dynamical systems with complicated behavior. Understanding the inner structure of recurrence is challenging, especially if the system has many degrees of freedom and is subject to noise. We…

The purpose of this book is to provide an introduction to period theory and then to place it within the matrix of recursive function theory.

The periods of the three-form on a Calabi-Yau manifold are found as solutions of the Picard-Fuchs equations; however, the toric varietal method leads to a generalized hypergeometric system of equations which has more solutions than just the…