The Poincaré conjecture can be understood by analogy with the case in two dimensions. A two-dimensional space, or surface, is like a bubble made from an infinitely thin film of soap. If the bubble is ...

image: a, Schematic of the proposed all-in-one polarizer that can function at an arbitrary position on the Poincaré sphere by design based on a dielectric metasurface composed of dimerized nanopillars ...

The never-knowingly-undersold Chinese news agency Xinhua is reporting that a team of Chinese scientists has solved Poincaré's Conjecture, one of the longest-outstanding mathematical problems that is ...

We aim to create a “Poincaré interface”, which can highly efficiently and freely convert photon polarization represented by a Poincaré sphere to electron spin represented by a Bloch sphere, by ...

A sphere is a sphere, right? Yes, if you mean a globe or a beach ball – what mathematicians call a two-dimensional sphere – but not if you are talking about a sphere in seven dimensions. Now the ...