Dennis Sullivan, a mathematician at Stony Brook University, has been awarded the Abel Prize, one of the highest honours in mathematics, for his work on topology and dynamical systems. The prize committee recognised Sullivan “for his groundbreaking contribution to topology” — the study and classification of shapes — as well as his expertise in unlocking a slew of mathematical problems from a geometric perspective.

Sullivan spent most of his entire career understanding topological spaces called manifolds. His research was oriented towards decoding such shapes in higher dimensions. He came up with a complete classification of manifolds of a particular type in five or more dimensions and made huge strides on a problem related to different ways of dividing manifolds into smaller triangular pieces. In the process, he furthered surgery theory (changing one manifold into another by cutting and regluing pieces).

In the early 2000s, Sullivan and his wife Moira Chas, a mathematician at Stony Brook, developed a new way to classify manifolds by studying loops and paths on their surfaces.

He then fused his interests in topology and dynamical systems and is now probing fluid flows from a topological perspective.