The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions by Yau Shing-Tung & Nadis Steve

Author:Yau, Shing-Tung & Nadis, Steve [Yau, Shing-Tung]
Language: eng
Format: mobi
ISBN: 9780465022663
Publisher: Basic Books
Published: 2010-08-11T16:00:00+00:00

Some would consider this last point debatable—and perhaps an overstatement. But SYZ has already been used—by Kontsevich and Yan Soibelman of Kansas State University, for instance—to prove a specific example of homological mirror symmetry, the other leading attempt at a fundamental mathematical description of mirror symmetry.

Homological mirror symmetry was first unveiled by Kontsevich in 1993 and has been developing ever since, sparking considerable activity in both physics and math. Mirror symmetry, as originally formulated, didn’t make much sense to mathematicians, as it concerned two different manifolds giving rise to the same physics. But as Soibelman explains, “in mathematics, there really is no concept of a physical theory associated with manifolds X and X′. So Kontsevich has tried to make that statement mathematically precise,” expressing it in a manner that is not tied to physics.40

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