Related papers: Olmec mirrors: an example of archaeological Americ…
This note briefly reviews the {\it Mirror Principle} as developed in the series of papers \LLYI\LLYII\LLYIII\LLYIV\LCHY. We illustrate this theory with a few new examples. One of them gives an intriguing connection to a problem of counting…
The array of micro-prisms was described by model of multi-period blazed gratings consisting of triangular apertures. The origins of hexagram-shaped diffraction patterns were interpreted based on multiple-beam interference and diffraction…
In this paper we study Seidel's mirror map for abelian and Kummer surfaces. We find that mirror symmetry leads in a very natural way to the classical parametrization of Kummer surfaces in $\P^3$. Moreover, we describe a family of embeddings…
In this article, we revisit the classical McKay correspondence via homological mirror symmetry. Specifically, we demonstrate how this correspondence can be articulated as a derived equivalence between the category of vanishing cycles…
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…
We review various constructions of mirror symmetry in terms of Landau-Ginzburg orbifolds for arbitrary central charge $c$ and \CY\ hypersurfaces and complete intersections in toric varieties. In particular it is shown how the different…
We present a construction of noncommutative double mirrors to complete intersections in toric varieties. This construction unifies existing sporadic examples and explains the underlying combinatorial and physical reasons for their…
The visible orientation of human eyes creates some transparency about people's spatial attention and other mental states. This leads to a dual role of the eyes as a means of sensing and communication. Accordingly, artificial eye models are…
It is shown how repeated observations of the sunset from various points up a tall building can be used to determine the Earth's radius. The same observations can also be used, at some latitudes, to deduce an approximate value for the amount…
How can we tell whether an image has been mirrored? While we understand the geometry of mirror reflections very well, less has been said about how it affects distributions of imagery at scale, despite widespread use for data augmentation in…
The device for injecting into a compact cyclotron is known as an inflector. The oldest simplest version is an electrostatic mirror. From the equations of motion through I derive the geometry of the mirror. Also the (1983 Bellomo et al.)…
An ancient solar observatory is composed by thirteen towers lined on a hill of a coastal desert of Peru. This is the Chankillo observatory. Here we discuss it, showing some simulations of the local sun direction. An analysis of the…
The traditional cultures of Aboriginal Australians include a significant astronomical component, which is usually reported in terms of songs or stories associated with stars and constellations. Here we argue that the astronomical components…
This article describes two new families of uniform polyhedra as well as the construction of the models of some of them. It is possible that these families have been discovered before, but I have been unable to find any publication about it.…
In this article we propose an original classification method for unobscured imaging systems unfolded in two dimensions. This classification is based on a study of off-axis properties, and relies on topology and algorithm of real algebraic…
Using our results about Lorentzian Kac--Moody algebras and arithmetic mirror symmetry, we give six series of examples of lattice-polarized K3 surfaces with automorphic discriminant.
We study some topological properties of attractors.
Within classical optics, one may add microscopic "roughness" to a macroscopically flat mirror so that parallel rays of a given angle are reflected at different outgoing angles. Taking the limit (as the roughness becomes increasingly…
This paper describes the evolution of aspects of differential and algebraic gometry from the mid 17th century till the end of the 18th century.
This is an editorial article based on the reseaches on the Ising model over the last 100 years.