Related papers: Invisibility and Inverse Problems
This note being devoted to some aspects of the inverse problem of representation theory contains a new insight into it illustrated by two topics. The attention is concentrated on the manner of representation of abstract objects by the…
Talk given at ICM '98, Berlin, reviewing some of the recent developments in understanding of string theory for a mathematical audience (to appear in Documenta Mathematica).
In these lectures I give an introduction to the time-dependent approach to inverse scattering, that has been developed recently. The aim of this approach is to solve various inverse scattering problems with time-dependent methods that…
As invisibility cloaking has recently become experimental reality, it is interesting to explore ways to reveal remaining imperfections. In essence, the idea of most invisibility cloaks is to recover the optical path lengths without an…
This list of problems arose as a collaborative effort among the participants of the Arbeitsgemeinschaft on Mathematical Quasicrystals, which was held at the Mathematisches Forschungsinstitut Oberwolfach in October 2015. The purpose of our…
In this note devoted to some aspects of the inverse problem of representation theory the attention is concentrated on the interrelations between various algebraic structures (algebras with operators) unraveled by different solutions of the…
A solution to the inversion problem of scattering would offer aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems. Powerful algorithms are increasingly being…
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
Recent advancements in computational inverse design have begun to reshape the landscape of structures and techniques available to nanophotonics. Here, we outline a cross section of key developments at the intersection of these two fields:…
The formalism of quantum systems with diagonal singularities is applied to describe scattering processes. Well defined states are obtained for infinite time, which are related to a ''weak form'' of intrinsic irreversibility. Real and…
The approximate cloaking is investigated for time-harmonic Maxwell's equations via the approach of transformation optics. The problem is reduced to certain boundary effect estimates due to an inhomogeneous electromagnetic inclusion with an…
This contribution to the concluding session at IAU Symposium 205 offered comments on some current controversies, including the scientific status of the ''multiverse'' concept and on the prospects for cosmology in the coming decade.
Blur is an image degradation that is difficult to remove. Invariants with respect to blur offer an alternative way of a~description and recognition of blurred images without any deblurring. In this paper, we present an original unified…
This is a collection of open problems from workshop "Differential Geometry, Billiards, and Geometric Optics" at CIRM on October 4-8, 2021.
In this talk, after a short phenomenological introduction on glasses, I will describe some recent progresses that have been done in glasses using the replica method in the definition and in the evaluation of the configurational entropy (or…
The problems we address in this paper are the spectral theory and the inverse problems associated with Laplacians on non-compact Riemannian manifolds and more general manifolds admitting conic singularities. In particular, we study the…
Solutions for the fields in a coated cylinder where the core radius is bigger than the shell radius are seemingly unphysical, but can be given a physical meaning if one transforms to an equivalent problem by unfolding the geometry. In…
Talk at the 25th Johns Hopkins Workshop "2001: A Relativistic Spacetime Odyssey", Firenze September 2001.
The proliferation of machine learning (ML) has drawn unprecedented interest in the study of various multimedia contents such as text, image, audio and video, among others. Consequently, understanding and learning ML-based representations…
I will present here my perception on the status of Deep Inelastic Scattering physics, as I have further developed it during this Workshop, together with a number of comments on the results that have impressed me most during this week. I…