Related papers: Hyperbolic reflections as fundamental building blo…

We consider hyperbolic projections of orbits of holomorphic self-maps of the unit disc, onto curves landing on the unit circle with a given angle. We show that under certain, necessary, assumptions, the projections exhibit monotonicity…

A reflection mapping is a singular holomorphic mapping obtained by restricting the quotient mapping of a complex reflection group. We study the analytic structure of double point spaces of reflection mappings. In the case where the image is…

We examine the optical properties of two different configurations of a cylindrical device made from a hyperbolic metamaterial with optical axis defined by circular and radial director fields. The hyperbolic metamaterial is an uniaxial…

We describe the action of a plane interface between two semi-infinite media in terms of a transfer matrix. We find a remarkably simple factorization of this matrix, which enables us to express the Fresnel coefficients as a hyperbolic…

Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…

Polaritons travelling along a hyperbolic medium's surface have recently sparked significant interest in nanophotonics for the unprecedented manipulation ability on light at the nanoscale in a planar way, promising potential nano-optical…

In this thesis, I am going to consider Bernoulli percolation on graphs admitting vertex-transitive actions of groups of isometries of d-dimensional hyperbolic spaces H^d. In the first chapter, I give an overview concerning percolation and…

We consider links that are alternating on surfaces embedded in a compact 3-manifold. We show that under mild restrictions, the complement of the link decomposes into simpler pieces, generalising the polyhedral decomposition of alternating…

Computer vision tasks such as image classification, image retrieval and few-shot learning are currently dominated by Euclidean and spherical embeddings, so that the final decisions about class belongings or the degree of similarity are made…

We consider here a generalization of a well known discrete dynamical system produced by the bisection of reflection angles that are constructed recursively between two lines in the Euclidean plane. It is shown that similar properties of…

We review the properties of hyperbolic metamaterials and show that they are promising candidates as substrates for nano-imaging, nano-sensing, fluorescence engineering and for controlling thermal emission. Hyperbolic metamaterials can…

In this article, we prove that the commensurability class of a closed, orientable, hyperbolic 3-manifold is determined by the surface subgroups of its fundamental group. Moreover, we prove that there can be only finitely many closed,…

We introduce and study the notions of hyperbolically embedded and very rotating families of subgroups. The former notion can be thought of as a generalization of the peripheral structure of a relatively hyperbolic group, while the later one…

We introduce a simple autoencoder based on hyperbolic geometry for solving standard collaborative filtering problem. In contrast to many modern deep learning techniques, we build our solution using only a single hidden layer. Remarkably,…

Hyperbolic Metamaterials (HMMs) continue to be intriguing due to their applications in super resolution imaging and spontaneous emission control. One of the successful realizations of HMMs is a layered metal-dielectric film. Despite the…

Here we study the space of real hyperbolic plane curves that are invariant under actions of the cyclic and dihedral groups and show they have determinantal representations that certify this invariance. We show an analogue of Nuij's theorem…

The geometric representation at a fixed frequency of the wavevector (or dispersion) surface $\omega(\vec k)$ for lossless, homogeneous dielectric--magnetic uniaxial materials is explored, when the elements of the relative permittivity and…

Multilayer networks offer a powerful framework for modeling complex systems across diverse domains, effectively capturing multiple types of connections and interdependent subsystems commonly found in real world scenarios. To analyze these…

We introduce a simple theoretical model that describes the interaction of light with optical metamaterials in terms of interfering optical plane waves. In this model, a metamaterial is considered to consist of planar arrays of densely…

We theoretically study the propagation of large-wavevector waves (volume plasmon polaritons) in multilayer hyperbolic metamaterials with two levels of structuring. We show that when the parameters of a subwavelength metal-dielectric…