Related papers: A Global Crystalline Period Map
Crystalline materials can form different structural arrangements (i.e. polymorphs) with the same chemical composition, exhibiting distinct physical properties depending on how they were synthesized or the conditions under which they…
A construction is given of Markov partitions for some rational maps, which persist over regions of parameter space, not confined to single hyperbolic components. The set on which the Markov partition exists, and its boundary, are analysed.
We consider the "occult" period maps into ball quotients which exist for the moduli spaces of cubic surfaces, cubic threefolds, non-hyperelliptic curves of genus three and four. These were constructed in the work of Allcock/Carlson/Toledo,…
In this note, we study the delooping of spaces and maps in homotopy type theory. We show that in some cases, spaces have a unique delooping, and give a simple description of the delooping in these cases. We explain why some maps, such as…
Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of…
Determining the range of complex maps plays a fundamental role in the study of several complex variables and operator theory. In particular, one is often interested in determining when a given holomorphic function is a self-map of the unit…
This tutorial offers a comprehensive overview of photonic time crystals - artificial materials whose electromagnetic properties are periodically modulated in time at scales comparable to the oscillation period of light while remaining…
The period set of a dynamical system is defined as the subset of all integers $n$ such that the system has a periodic orbit of length $n$. Based on known results on the intersection of period sets of torus maps within a homotopy class, we…
We introduce the idea of temporal graphs, a representation that encodes temporal data into graphs while fully retaining the temporal information of the original data. This representation lets us explore the dynamic temporal properties of…
Crystalline interfaces are of highly importance in many practical applications. To conduct effective simulation and analysis for coincident site lattice (CSL) interfaces, effective programmes are of high demand in building their CSL…
Crystallization of the amorphous phases into metastable crystals plays a fundamental role in the formation of new matter, from geological to biological processes in nature to synthesis and development of new materials in the laboratory.…
This informal note provides some elementary examples to motivate the local structural results of [1] on the moduli space of genus one stable maps to projective space. The hope is that these examples will be helpful for graduate students to…
We study the dynamics of piecewise conformal maps in the Riemann sphere. The normality and chaotic regions are defined and we state several results and properties of these sets. We show that the stability of these piecewise maps is related…
A temporal graph is a data structure, consisting of nodes and edges in which the edges are associated with time labels. To analyze the temporal graph, the first step is to find a proper graph dataset/benchmark. While many temporal graph…
Moduli spaces of bounded local $G$-shtukas are a group-theoretic generalization of the function field analog of Rapoport and Zink's moduli spaces of $p$-divisible groups. In this article we generalize some very prominent concepts in the…
We construct holomorphic maps with a Siegel disk whose boundary is not locally connected (and is an indecomposable continuum), yet compactly contained in the domain of definition of the map. Our examples are injective and defined on a…
We use the p-adic local Langlands correspondence for GL_2(Q_p) to explicitly compute the reduction modulo p of crystalline representations of small slope, and give applications to modular forms.
The Earth's surface is subject to complex and dynamic processes, ranging from large-scale phenomena such as tectonic plate movements to localized changes associated with ecosystems, agriculture, or human activity. Satellite images enable…
We introduce a new class of out-of-equilibrium noninteracting topological phases, the topological space-time crystals. These are time-dependent quantum systems which do not have discrete spatial translation symmetries, but instead are…
Periodic splines are a special kind of splines that are defined over a set of knots over a circle and are adequate for solving interpolation problems related to closed curves. This paper presents a method of implementing the objects…