Related papers: Equitable Mirrors
These notes are devoted to explaining aspects of the mirror manifold problem that can be naturally understood from the point of view of topological field theory. Basically this involves studying the topological field theories made by…
Recent advances in the physics of resonant optical metasurfaces allowed to realize the so-called maximum chirality of planar structures by engineering their geometric parameters. Here we employ bilayer membrane metasurfaces with a square…
See http://www.youtube.com/watch?v=izbGXdjvK_I for a YouTube video showing part of the results in this paper.We will consider surfaces whose mean curvature at a point is a linear function of the square of the distance from that point to the…
We report the realisation of a high-finesse open-access cavity array, tailored towards the creation of multiple coherent light-matter interfaces within a compact environment. We describe the key technical developments put in place to…
We survey some results on real rational surfaces focused on their topology and their birational geometry.
K-frame theory was recently introduced to reconstruct elements from the range of a bounded linear operator K in a separable Hilbert space. This significant property is worthwhile especially in some problems arising in sampling theory. Some…
Recent advances in nanofabrication and optical control have garnered tremendous interest in multi-qubit-cavity systems. Here we analyze a spin-glass version of such a nanostructure, solving analytically for the phase diagrams in both the…
We develop a theory and an algorithm for constructing minimal-degree polynomial moving frames for polynomial curves in an affine space. The algorithm is equivariant under volume-preserving affine transformations of the ambient space and the…
In this paper, we establish equivariant mirror symmetry for the weighted projective line. This extends the results by B. Fang, C.C. Liu and Z. Zong, where the projective line was considered [{\it Geometry \& Topology} 24:2049-2092, 2017].…
The study of 3d mirror symmetry has greatly enhanced our understanding of various aspects of 3d $\mathcal{N}=4$ theories. In this paper, starting with known mirror pairs of 3d $\mathcal{N}=4$ quiver gauge theories and gauging discrete…
In this article, we prove new stability results for almost-Einstein hypersurfaces of the Euclidean space, based on previous eigenvalue pinching results. Then, we deduce some comparable results for almost umbilical hypersurfaces.
In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of coefficients preserving…
Semi-Equivelar maps are generalizations of Archimedean Solids (as are equivelar maps of the Platonic solids) to the surfaces other than $2-$Sphere. We classify some semi equivelar maps on surface of Euler characteristic -1 and show that…
Layered metal-dielectric metamaterials have filtering properties both in the frequency domain and in the spatial frequency domain. Engineering their spatial filtering response is a way of designing structures with specific diffraction…
The purpose of this work is to examine the structure of optimal dual fusion frames and get more exibility in the use of dual fusion frames for erasures of subspaces. We deal with optimal dual fusion frames with respect to different…
A projective mirror polyhedron is a projective polyhedron endowed with reflections across its faces. We construct an explicit diffeomorphism between the moduli space of a mirror projective polyhedron with fixed dihedral angles in…
Additive manufacturing (AM; 3D printing) has clear benefits in the production of lightweight mirrors for astronomy: it can create optimised lightweight structures and combine multiple components into one. New capabilities in AM ceramics,…
We survey different classification results for surfaces with parallel mean curvature immersed into some Riemannian homogeneous four-manifolds, including real and complex space forms, and product spaces. We provide a common framework for…
Mirrors are one of the most elementary and ubiquitous components of optical systems. They use a sharp refractive index contrast to provide the basic capability of reflecting light. Motivated by recent developments of photonic time-varying…
In this paper, we introduce round and sleek topological spaces and study their properties.