Related papers: Completions of period mappings: progress report
We demonstrate the existence of quasiconformal mappings on closed manifolds that cannot be decomposed as a composition of mappings with arbitrarily small conformal distortion.
We propose an analog of the Satake--Baily--Borel compactification and Borel's extension theorem for arbitrary period maps. The proposed analog is constructed as a proper topological completion of the period map. It is conjectured that the…
Let $f$ be a piecewise continuous and monotonic map on the interval with at most finitely many discontinuities and turning points. In this paper we study properties about this class of maps and show its main difference from the continuous…
This is neither a summary talk (too much for too short a talk) nor a conclusion (a gigantic work is in progress and we are not at the end of a particular phase), rather an overview of the field as reflected at this Conference.
Process maps provide a high-level overview of an organisation's business processes. While used for many years in different shapes and forms, there is little shared understanding of the concept and its relationship to enterprise…
The differential geometric aspects of Geometric Phases are reviewed.
The crystalline period map is a tool for linearizing $p$-divisible groups. It has been applied to study the Langlands correspondences, and has possible applications to the homotopy groups of spheres. The original construction of the period…
The exposition has been significantly altered, hopefully improved.
There are various concepts of structure preserving mappings in geometry. It is the aim of the present paper to give a survey on geometrical characterizations of some of those mappings. We discuss the results for projective spaces in some…
We survey some results on toric topology.
We present, to the best of the authors' knowledge, all known results for the (planar) crossing numbers of specific graphs and graph families. The results are separated into various categories; specifically, results for general graph…
Simple constructions are given for finite semifields that include as special cases both old semifields and recently constructed semifields.
Transitivity, the existence of periodic points and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that for graphs that are not trees, for every $\varepsilon>0,$ there exist (complicate)…
The full evolution during the late periods of the condensation process is described in the analytical form. The process is split into several periods and for every period the simple approximate solution is given.
Period mappings were introduced in the sixties [G] to study variation of complex structures of families of algebraic varieties. The theory of tautological systems was introduced recently [LSY,LY] to understand period integrals of algebraic…
This a slightly expended version of my habilitation thesis, which is an overview of my research activities during the last 4 years, written in a rather informal style.
We introduce {\it twist unimodal maps} of the interval and describe their structure. Sufficient conditions for the growth of over-rotation interval in families of maps are given.
In this survey we overview known results and get several new results on digraph compositions which generalize several classes of digraphs, such as quasi-transitive digraphs. After an introductory section, the paper is divided into six…
We prove that the image of period map is algebraic, as conjectured by Griffiths.
We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that…