On paper, the calculation would cover an area the size of Manhattan. But an international group of 18 mathematicians and computer scientists, including two from MIT, has found a more practical way to calculate the inner workings of E8, one of the most complicated symmetrical structures in mathematics. Mathematics professor David Vogan and Dan Ciubotaru, an instructor in the math department, were among those who put the supercomputer Sage through a 77-hour computation to calculate the 200 billion numbers in E8’s character table, generating a 60-gigabyte file.
E8 is an example of a Lie group–a continuous symmetry group whose structure is always transforming yet, like a sphere rotating around an axis, always looks the same. All but five Lie groups fall into one of four classes related to linear algebra and Euclidean geometry. E8 is the most complex of these five “exceptional” Lie groups. It describes the symmetries of a 57-dimensional object that can be rotated in 248 ways without changing its appearance. Calculating its character table–a 453,060-by-453,060 matrix that describes all the ways E8 can appear as a symmetry group–is just one important step toward understanding all Lie groups, says Vogan.
This computer-generated illustration is of the E8 root system, an arrangement of 240 vectors in an eight-dimensional space. The image is a two-dimensional projection of that eight-dimensional arrangement.
Embracing CX in the metaverse
More than just meeting customers where they are, the metaverse offers opportunities to transform customer experience.
Identity protection is key to metaverse innovation
As immersive experiences in the metaverse become more sophisticated, so does the threat landscape.
The modern enterprise imaging and data value chain
For both patients and providers, intelligent, interoperable, and open workflow solutions will make all the difference.
Scientists have created synthetic mouse embryos with developed brains
The stem-cell-derived embryos could shed new light on the earliest stages of human pregnancy.
Get the latest updates from
MIT Technology Review
Discover special offers, top stories, upcoming events, and more.