Through a field called geometric topology, mathematicians like me study all possible spaces in all dimensions. Whether trying to design secure sensor networks, mine data or use origami to deploy ...

Whether trying to design secure sensor networks, mine data or use origami to deploy satellites, the underlying language and ideas are likely to be that of topology.

Topological insulators are materials that are insulating in their interior but can support the flow of electrons on their surface. The underlying cause is time-reversal symmetry: their physics is ...

For example, the surface of a giant doughnut is another 2D space. Through a field called geometric topology, mathematicians like me study all possible spaces in all dimensions. Whether trying to ...

For example, the surface of a giant doughnut is another 2D space. Through a field called geometric topology, mathematicians like me study all possible spaces in all dimensions. Whether trying to ...

The surface of a torus (the shape of our breakfast donut), for example, offers another perspective of what a 2D space could be. Mathematicians, through geometric topology, explore these spaces in ...

Specifically, the linear dispersion around Dirac points underpins the formation of robust surface states in topological insulators and contributes to the exotic electronic properties of topological ...

Cellular topography could cause an underappreciated problem in this respect as well. On a smooth surface the tag and molecule probably maintain a stable alignment, but topography produces an ...

like a giant 3D version of the 2D beach ball surface or something even more exotic than that. While you don’t need topology to determine that you are living on something like a giant beach ball ...

What other possible spaces might you be living on? That is, what other spaces around you are 2D? For example, the surface of a giant doughnut is another 2D space. Through a field called geometric ...