Related papers: Invisibility and Inverse Problems
Geometric complexity theory (GCT) is an approach to the $P$ vs. $NP$ and related problems. A high level overview of this research plan and the results obtained so far was presented in a series of three lectures in the Institute of Advanced…
We study the approximate cloaking via transformation optics for electromagnetic waves in the time harmonic regime in which the cloaking device {\it only} consists of a layer constructed by the mapping technique. Due to the fact that…
In a recent comment arxiv:1310.1503 Miller et al. noted that a cloak we previously presented (Scientific Reports 3, 2328) that exploits a scattering cancellation technique to render an optically small dielectric particle invisible suffers…
The alignments of galaxies across the large-scale structure of the Universe are known to be a source of contamination for gravitational lensing, but they can also probe cosmology and the physics of galaxy evolution in many ways. In this…
These notes are a considerably revised and expanded version of expository lectures given at the Fields Institute Workshop on "Nonlinear Dispersive Partial Differential Equations and Inverse Scattering" in August 2017. We give a complete and…
This is an extended version of notes prepared for the talk at the conference "Rajchman-Zygmund-Marcinkiewicz 2000" based on recent works of the authors.
The electromagnetic implementation of cloaking, the hiding of objects from sight by diverting and reassembling illuminating electromagnetic fields has now been with us ten years, while the notion of hiding events is now five. Both schemes…
Transformation optics is a design tool that connects geometry of space and propagation of light. Invisibility cloaking is a corresponding benchmark example. Recent experiments at optical frequencies have demonstrated cloaking for the light…
We develop and apply an optimization method to design invisibility cloaks. Our method is based on minimizing the forward scattering amplitude of the cloaked object, which by the optical theorem, is equivalent to the total cross section. The…
Recent observations indicate that the Universe is not transparent but partially opaque due to absorption of light by ambient cosmic dust. This implies that the Friedmann equations valid for the transparent universe must be modified for the…
Microscopy and optical imaging are drastically limited by the inhomogeneities encountered by the light while propagating from the object of interest to the detection system. In this context, adaptive optics and wavefront manipulation are…
This is a renovated list of open problems, to appear in: "Affine Algebraic Geometry" conference Proceedings volume in Contemporary Mathematics series of the Amer. Math. Soc. Ed. by Jaime Gutierrez, Vladimir Shpilrain, and Jie-Tai Yu.
The key challenge in current research into electromagnetic cloaking is to achieve invisibility over an extended bandwidth. There has been significant progress towards this using the idea of cloaking by sweeping under the carpet of Li and…
Summary of a talk given at the International Seminar "Analysis of spectral invariants and related operator theory", Tokyo University of Science, Unga Campus, 5-6 Oct. 2009
The inverse scattering transform is developed to solve the Maxwell-Bloch system of equations that describes two-level systems with inhomogeneous broadening, in the case of optical pulses that do not vanish at infinity in the future. The…
Transformation optics constructions have allowed the design of cloaking devices that steer electromagnetic, acoustic and quantum waves around a region without penetrating it, so that this region is hidden from external observations. The…
The GRavitational lEnsing Accuracy Testing 2008 (GREAT08) Challenge focuses on a problem that is of crucial importance for future observations in cosmology. The shapes of distant galaxies can be used to determine the properties of dark…
This is the text of a series of five lectures given by the author at the "Second Annual Spring Institute on Noncommutative Geometry and Operator Algebras" held at Vanderbilt University in May 2004. It is meant as an overview of recent…
The structure and potential of a complex gravitational lens is reconstructed using the perturbative method presented in Alard 2007, MNRAS, 382L, 58; Alard 2008, MNRAS, 388, 375. This lens is composed of 6 galaxies belonging to a small…
As per organizers' request, my talk at the 11th Marcel Grossmann Conference consisted of two parts. In the first, I illustrated recent advances in loop quantum gravity through examples. In the second, I presented an overall assessment of…