Related papers: Mirror Symmetry And Some Applications
We demonstrate in microwave measurements the broadband enhancement of transmission through an opaque barrier due to mirror symmetry. This enhancement relies on constructive interference between mirror scattering paths resulting from strong…
A brief summary of recent developments in mathematical diffraction theory is given. Particular emphasis is placed on systems with aperiodic order and continuous spectral components. We restrict ourselves to some key results and refer to the…
We investigate the effect of a mirror-symmetry plane in multiple-scattering media under plane-wave illumination along the symmetry plane. Designed and fabricated samples' optical transport properties are compared quantitatively with…
The problem of mirror-reflection symmetry (MRS) and time-reversal symmetry (TRS) in our world is discussed. The opinion is expressed, that well-known experiments on parity violation and CP-violation can be treated as signals of some new,…
3d mirror symmetry is a mysterious duality for certian pairs of hyperk\"ahler manifolds, or more generally complex symplectic manifolds/stacks. In this paper, we will describe its relationships with 2d mirror symmetry. This could be…
This is a very brief survey of some results in the geometry of string duality delivered at a lecture given at ICM 1998, Berlin. String Duality is the statement that one kind of string theory compactified on one space is equivalent in some…
Aspects of duality and mirror symmetry in string theory are discussed. We emphasize, through examples, the importance of loop spaces for a deeper understanding of the geometrical origin of dualities in string theory. Moreover we show that…
We extend a result proved in \cite{Col} for mirror symmetries of planar systems to measure-preserving non-linear reversibilities of $n$-dimensional systems, dropping the analyticity and nondegeneracy conditions.
In this essay we give an introduction to conformal symmetry, based on the example of the Yamabe operator and its use in conformal differential geometry, and in representation theory.
The first part of this paper is a survey of mathematical results on mirror symmetry phenomena between Hitchin systems for Langlands dual groups. The second part introduces and discusses multiplicity algebras of the Hitchin system on…
Mirror symmetry, a phenomenon in superstring theory, has recently been used to give tentative calculations of several numbers in algebraic geometry. In this paper, the numbers of lines and conics on various hypersurfaces which satisfy…
These short (personal) notes appeared as the result of my attempt to address the question raised in the title.
Symmetry plays a central role in quantum field theory. Recent developments include symmetries that act on defects and other subsystems, and symmetries that are categorical rather than group-like. These generalized notions of symmetry allow…
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…
This review describes the history of discovery of violation of spatial parity P, charge conjugation parity C, combined parity CP. The hypothesis of existence of mirror particles was called upon by its authors to restore the symmetry between…
This survey was written for the Current Developments in Mathematics conference, 2012, and is an updating of my article "The Strominger-Yau-Zaslow conjecture: From torus fibrations to degenerations," in the Seattle 2005 proceedings. We trace…
We use a relative Fourier-Mukai transform on elliptic K3 surfaces $X$ to describe mirror symmetry. The action of this Fourier-Mukai transform on the cohomology ring of $X$ reproduces relative T-duality and provides an infinitesimal isometry…
These notes are devoted to explaining aspects of the mirror manifold problem that can be naturally understood from the point of view of topological field theory. Basically this involves studying the topological field theories made by…
Motivated by the recent work of Kachru-Vafa in string theory, we study in Part A of this paper, certain identities involving modular forms, hypergeometric series, and more generally series solutions to Fuchsian equations. The identity which…
All known string theory models may be obtained as partial fermionization, projection and background Ans\"atze from the original, purely bosonic string theory. The latter theory in turn has been recently shown to describe a chirally and…