Related papers: Equitable Mirrors
This is a survey paper on our recent works concerning the classification of positively curved homogeneous Finsler spaces, and some related topics. At the final part, we present some open problems in this field.
We give a survey of results on the geometry of complex algebraic Q-acyclic surfaces, so-called 'Q-homology planes', including some recent results.
In talk I will review the theoretical results that have been obtained for spin glasses, paying a particular attention to finite dimensional spin glasses. I will concentrate my attention on the formulation of the mean field approach and on…
Carbon fibre composite technology for lightweight mirrors is gaining increasing interest in the space- and ground-based astronomical communities for its low weight, ease of manufacturing, excellent thermal qualities and robustness. We…
We discuss applications of minimal surfaces to comparison geometry.
The quest for regular models of arithmetic surfaces allows different viewpoints and approaches: using valuations or a covering by charts. In this article, we sketch both approaches and then show in a concrete example, how surprisingly…
In this letter, we show that a perfect lens can be employed to make multiple objects appear like only one in the far field, leading to a new concept of illusion optics. Numerical simulations are performed to verify the functionalities for…
Resonant dielectric planar structures can interact selectively with light of particular helicity thus providing an attractive platform for chiral flat optics. The absence of mirror-symmetry planes defines geometric chirality, and it remains…
In this paper we discuss some affine properties of convex equal-area polygons, which are convex polygons such that all triangles formed by three consecutive vertices have the same area. Besides being able to approximate closed convex smooth…
We give cohomological criteria for logarithmic good reduction of elliptic surfaces up to modification. Along the way, we prove several more general results about such surfaces in positive characteristic, as well as about log smooth…
Progressive addition lenses contain a surface of spatially-varying curvature, which provides variable optical power for different viewing areas over the lens. We derive complete compatibility equations that provide the exact magnitude of…
Dielectric mirrors comprising thin-film multilayers are widely used in optical experiments because they can achieve substantially higher reflectance compared to metal mirrors. Here we investigate potential problems that can arise when…
We report on recent progress in understanding mirror symmetry. Some of more recent generalizations and applications are also presented. --- A contribution to the Proceedings of ``Strings 2001'' at Mumbai, India.
This is a report on the recent work "Mirror symmetry for exceptional unimodular singularities" joint with Changzheng Li, Si Li and Yefeng Shen.
Our goal is to provide a survey of some topics in quasiconformal analysis of current interest. We try to emphasize ideas and leave proofs and technicalities aside. Several easily stated open problems are given. Most of the results are joint…
We report the results of a recent search for the lowest value of thermal noise that can be achieved in LIGO by changing the shape of mirrors, while fixing the mirror radius and maintaining a low diffractional loss. The result of this…
Multimode interference reflectors (MIRs) were recently introduced as a new type of photonic integrated devices for on-chip, broadband light reflection. In the original proposal, different MIRs were demonstrated based on total internal…
Optical cavities are frequently used in quantum technologies to enhance light matter interactions, with applications including single photon generation and entanglement of distant emitters. The Fabry-P\'{e}rot resonator is a popular choice…
We review recent findings on spin glass models. Both the equilibrium properties and the dynamic properties are covered. We focus on progress in theoretical, in particular numerical, studies, while its relationship to real magnetic materials…
We investigate equivariant birational geometry of rational surfaces and threefolds from the perspective of derived categories.