PHYSICAL NETWORK

What if a network has a shape? Using string theory, we explore the possibility of equipping a network with differential geometry, by promoting the network to a smooth **manifold**. We find that a minimization principle of not only the wiring length but also higher-dimensional manifold measures (such as surface area or volume) can explain some universal morphologies of biological systems that have long been observed, yet not theorized.

QUANTUM NETWORK

How to efficiently distribute **quantum entanglement** between two or more distant nodes that are not directly linked (hence not directed entangled)? To answer this question, we need to understand the large-scale statistical behaviors of quantum networks—at a level deeper than ever before.

NETWORK OF NETWORKS

A network of networks contains multiple layers, each layer representing a network that is interdependent to other layers through bridge nodes and links. We are interested in the structual and dynamical behaviors of such a network of networks, analyzing them using a rich set of tools—from percolation theories to dynamical equations.