Emergent Hyperbolic Network Geometry

Emergent Hyperbolic Network Geometry

A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a ...

Emergent Complex Network Geometry

Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their d...

Hyperbolic Geometry

Instantons and Emergent Geometry

Gravity is a mysterious force; we still don’t know what gravity is. But recent developments from string and M theories gradually reveal an intriguing picture on gravity (for recent reviews, see, for example, [1, 2]): Gravity may be a collective phenomenon emergent from gauge fields. That is, the spin-two graviton might arise as a composite of two spin-one gauge bosons. Although the emergent gra...

Emergent Calabi-Yau geometry.

We show how the smooth geometry of Calabi-Yau manifolds emerges from the thermodynamic limit of the statistical mechanical model of crystal melting defined in our previous paper. In particular, the thermodynamic partition function of molten crystals is shown to be equal to the classical limit of the partition function of the topological string theory by relating the Ronkin function of the chara...