This story is a supplement to the feature "Rubik's Cube Inspired Puzzles Demonstrate Math's "Simple Groups"" which was printed in the July 2008 issue of Scientific American. All three new puzzles ...

Group theory, a cornerstone of modern algebra, provides a framework to explore the structure, symmetry, and internal operations of sets endowed with a binary operation. Central to this discipline is ...

We classify homogeneous Einstein metrics on compact irreducible symmetric spaces. In particular, we consider symmetric spaces with $\operatorname{rank}(M) > 1$, not isometric to a compact Lie group.

We show that every limit point of a Zariski dense discrete subgroup Γ of the isometry group of a symmetric space of noncompact type is conical if and only if Γ is convex cocompact.