Topological complexity is a central concept that bridges the abstract methodologies of algebraic topology with the practical challenges of robot motion planning. It provides a numerical invariant that ...

Molding the flow of light—whether confined to localized regions or propagating in free space—remains crucial for modern integrated photonics. The advancement of the multi-channel, programmable optical ...

Topological physics is a major research topic in modern science. The discovery of topological phases of matter has revolutionized how researchers think about electronic, photonic, and acoustic ...

On the left, the schematic illustration depicts the gluing rules of the Brillouin manifold, with a half-twist operation connecting the opposing faces. On the right, the BZ is divided into 64 blocks by ...