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

A framework for analyzing single-cell genomics data, in which geometrical properties are harnessed to obtain insights on cellular diversity, including precise clustering, clear visualizations, and ...

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 ...

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 ...

Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about. In the early 1800s, William Rowan Hamilton discovered a new kind of ...

Clean and complete geometry is important for successful 3D printing. A watertight mesh helps reduce common printing problems ...