In quantum mechanics, the geometry of quantum states has emerged as a powerful framework for understanding phenomena ranging ...

Quantum geometry describes quantum states in systems with changing system parameters, such as an electron spinning in a magnetic field whose direction is slowly changing. The state of the electron ...

How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of recent work by the ...

In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space. When you gaze out ...

Cycling culture is full of little idiosyncrasies. Some of them we love and respect, like the fact that a water bottle is a ...

Can you imagine the imprint a four-dimensional hexagon might leave as it passes through your three-dimensional kitchen table? Probably not, but some people can. One such person was mathematician ...

A hidden quantum geometry that distorts electron paths has finally been observed in real materials. This “quantum metric,” once thought purely theoretical, may revolutionize electronics, ...

A road bike frame is essentially three big tubes stuck together in a triangle, four thinner ones to support the rear wheel and a fork to hold the front wheel and allow it to turn. But it’s a lot more ...