Related papers: Invisibility and Inverse Problems
In this brief review I consider the advances made in weak gravitational lensing over the last 8 years, concentrating on the large scales - cosmic shear. I outline the theoretical developments, observational status, and the challenges which…
There is increasing interest in extended source effects in microlensing events, as probes of the unresolved sources. Previous work has either presumed a uniform source, or else required an approximate or numerical treatment of the…
This is a survey article, based on the author's lectures in the 2015 Current developments in Mathematics meeting; published in "Current developments in Mathematics". Version 2, references corrected and added.
Invisibility cloaks, a subject that usually occurs in science fiction and myths, have attracted wide interest recently because of their possible realization. The biggest challenge to true invisibility is known to be the cloaking of a…
This is a pedagogical account of the recent results of Brydges and Imbrie, described from the point of view of Grassmann integration. Some simple extensions are pointed out.
The invisibility cloak has been a long-standing dream for many researchers over the decades. The introduction of transformational optics has revitalized this field by providing a general method to design material distributions to hide the…
Transformation optics constructions have allowed the design of electromagnetic, acoustic and quantum parameters that steer waves around a region without penetrating it, so that the region is hidden from external observations. The material…
We examine additional symmetries of specific refraction index profiles that are used in the well-known phenomena of perfect imaging and cloaking.In the considered cases, the translation generator and the angular momentum are conserved. We…
An invisibility cloak that can hide an arbitrary object external to the cloak itself has not been devised before. In this Letter, we introduce a novel way to design a remote cloaking device that makes any object located at a certain…
We consider the determination of a conductivity function in a two-dimensional domain from the Cauchy data of the solutions of the conductivity equation on the boundary. We prove uniqueness results for this inverse problem, posed by…
We study approximate cloaking using transformation optics for electromagnetic waves in the time domain. Our approach is based on estimates of the degree of visibility in the frequency domain for all frequencies in which the frequency…
The present lectures were prepared for the Faro International Summer School on Factorization and Integrable Systems in September 2000. They were intended for participants with the background in Analysis and Operator Theory but without…
These are lecture notes from my talks at the "Current Developments in Mathematics" conference (Harvard, 2006). They cover a variety of topics involving symplectic cohomology. In particular, a discussion of (algorithmic) classification…
A review of some of the author's results in the area of inverse scattering is given. The following topics are discussed: 1) Property $C$ and applications, 2) Stable inversion of fixed-energy 3D scattering data and its error estimate, 3)…
We propose to use transformation optics to generate a general illusion such that an arbitrary object appears to be like some other object of our choice. This is achieved by using a remote device that transforms the scattered light outside a…
More than ten years ago Ikehata discovered two mathematical methods for the purpose of extracting information about the location and shape of unknown discontinuity embedded in a known background medium from observation data. The methods are…
These lectures give an introduction to Gravitational Lensing. We discuss lensing by point masses, lensing by galaxies, and lensing by clusters and larger-scale structures in the Universe. The relevant theory is developed and applications to…
Transformation optics (TO) is a powerful tool for the design of artiffcial materials with unprecedented optical properties. Here, we propose the approximation of TO structures of arbitrary shape by faceting, in which curved surfaces are…
These lectures have been given to particle physicists, mostly experimentalists and very briefly and at a pedestrian level review the problems of dark matter. The content of the lectures is the following: 1. Introduction. 2. Cosmological…
We highlight the correspondence between one-dimensional Lorentz transformations, which relate events observed from two distinct inertial reference frames, and ray transfer transformations in Gaussian optics. Specifically, we identify…