Xiaorui Sun of the University of Illinois, Chicago, has developed a method that can determine if two abstract mathematical groups are the same more quickly than with previous methods. Isomorphism, the study of abstract objects that appear to be the same despite superficial differences, has clear uses in computer science. Sun’s innovative approach allows him to divide groups into two pieces with different algorithmic methods applied to each part. Sun found that belonging to a special family of groups, he could execute this division with an improved method of $n^{(logn)^{5/6}}$ time complexity.
https://www.quantamagazine.org/computer-scientists-inch-closer-to-major-algorithmic-goal-20230623/