By adapting mathematical techniques used in particle physics, researchers in Germany have developed an approach that could ...

Second, Calabi-Yau manifolds are “Ricci-flat.” According to Albert Einstein’s general theory of relativity, the presence of matter or energy bends space-time, causing so-called Ricci curvature. Calabi ...

If we replace the spheres in curled-up space with these Calabi-Yau shapes, we end up with 10 dimensions: three spatial, plus the six of the Calabi-Yau shapes, plus one of time. If superstring ...

A manifold is a surface or space that can exist in any dimension ... On Christmas Day in 1976, Yau met with Calabi and another mathematician, who confirmed the validity of his proof, establishing the ...

A particle’s mass, the strength of a given force and other fundamental quantities depend on the shape, or geometry, of this convoluted space. String theorists soon made a remarkable discovery. By ...

Scientists have made the most accurate predictions yet of the gravitational waves produced when two black holes fly past each other.

Wiseman and Headrick (who works at Brandeis University) knew that a Calabi-Yau metric had to solve Einstein’s equations for empty space. A metric satisfying this condition guaranteed that a ...

The research reveals the surprising appearance of Calabi-Yau three-fold periods -- complex geometric structures from string theory and algebraic geometry -- within calculations of radiated energy ...

But if the universe contains compact, hidden extra dimensions in the shape of Calabi-Yau manifolds ... In one poem, titled “Ode to Space-Time,” Yau writes: So immense our puzzling universe ...