Related papers: Mirror Symmetry And Some Applications

We prove mirror symmetry for supersymmetric sigma models on Kahler manifolds in 1+1 dimensions. The proof involves establishing the equivalence of the gauged linear sigma model, embedded in a theory with an enlarged gauge symmetry, with a…

In recent years various results about locally symmetric manifolds were proven using probabilistic approaches. One of the approaches is to consider random manifolds by associating a probability measure to the space of discrete subgroups of…

We consider extending the visibility polygon of a given point $q$, inside a simple polygon $P$ by converting some edges of $P$ to mirrors. We will show that several variations of the problem of finding mirror-edges to add precisely $k$…

Stereo matching is one of the longest-standing problems in computer vision with close to 40 years of studies and research. Throughout the years the paradigm has shifted from local, pixel-level decision to various forms of discrete and…

We give an overview of recent developments in the theory of dimer models. The viewpoint we take is inspired by mirror symmetry. After an introduction to the combinatorics of dimer models, we will first look at dimers in dynamical systems…

We propose an algorithm to detect approximate reflection symmetry present in a set of volumetrically distributed points belonging to $\mathbb{R}^d$ containing a distorted reflection symmetry pattern. We pose the problem of detecting…

We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…

Nuclear supersymmetry is reviewed and some of its applications and extensions are discussed, together with a proposal for new, more stringent and precise tests to probe the supersymmetry classification, in particular, correlations between…

The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…

We prove that the mirror pairs constructed by Batyrev and Borisov have stringy mirror symmetry.

Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra…

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).

We solve the problem of equivariant mirror symmetry for O(-3)->P^2 for the (three) cases of one independent equivariant parameter. This gives a decomposition of mirror symmetry for local P^2 into that of three subspaces, each of which may…

These lectures are a brief introduction to supersymmetry.

An overview of some of the developments in string theory over the past two years is given, focusing on four topics: realistic (standard model like) models from string theory, geometric engineering and theories with fluxes, the gauge…

The solution of a fine tuning problem is one of the principal motivations of Supersymmetry. However experimental constraints indicate that many Supersymmetric models are also fine tuned (although to a much lesser extent). We review the…

I review some of the recent progress in two-dimensional string theory, which is formulated as a sum over surfaces embedded in one dimension.

We propose that light can break mirror symmetries and combining symmetries with a uniform time translation, and their breaking is characterized by an off-diagonal charge conductivity. Taking periodically driven graphene as an example, we…

We study ray optics in the context of double mirror systems, in the limit as the two mirrors approach one another (thin films). This leads to a novel set of differential equations on a mirror surface which have interesting structure as seen…

In this article we introduce a group-theoretical point of view for the design of magnetic optical achromats based on symmetry. As examples we use two-cell repetitive achromats and four-cell achromats employing mirror symmetry.