In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau manifolds. The term refers to a situation where two Calabi–Yau manifolds look very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory.

Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics.

Mirror symmetry is a proposed duality between symplectic geometry and complex geometry. In its full generality, the Mirror symmetry conjecture gives us two things: For every symplectic manifold X, a complex manifold X called the mirror of X (and vice versa.) Some in uential papers on mirror symmetry include [CXGP91] [Kon94], [SYZ96] and [GS03].

Overview of mirror symmetry Lecture 1, August 29, 2019 The course is topics in algebraic geometry. We will be doing some sort of mirror sym-metry. We will start with some historical overview. 1. Enumerative mirror symmetry Let X be a CY manifold. In particular we will focus on CY 3-folds. This means KX = detT X ≃OX is trivial as a holomorphic ...

In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry.

Mirror Symmetry. This thorough and detailed exposition is the result of an intensive month-long course that CMI held in the Spring of 2000. It provides a pedagogical introduction to the field of mirror symmetry from both a mathematical and physical perspective.

This course will focus on various aspects of mirror symmetry. It is aimed at students who already have some basic knowledge in symplectic and complex geometry (18.966, or equivalent). The geometric concepts needed to formulate various mathematical versions of mirror symmetry will be introduced along the way, in variable levels of detail and rigor.

mirrors. The SYZ conjecture helps us construct mirror pairs. Conjecture 3 (SYZ). For X,X∨ mirrors, they carry mutually dual fibrations by special Lagrangian tori, i.e. Tn X,(T∨)n X ∨ (5) B B Here, Ln ⊂ X is special Lagrangian if ω| L = 0 and Im Ω| L = 0, and T ∨ = Hom(π 1(T ),U(1)).

2025年1月31日 · Mirror symmetry is sometimes called bilateral symmetry. Most animals are very nearly bilaterally symmetric. Molecules without bilateral symmetry come in two varieties denoted L (laevo) and R (dextro), each of which is the mirror image of the other.

2021年6月21日 · Mirror symmetry. If I build the mirror image of an apparatus, it works the same albeit in a mirrored way. Warning: below we shall see violations of this symmetry.