The Norwegian Academy of Science and Letters has awarded the Abel prize for the year 2022 to American Mathematician Dennis Parnell Sullivan, who is with the Graduate School and University Center of the City University of New York and the State University of New York at Stony Brook. The citation mentions that the award has been given, “For his groundbreaking contributions to topology in its broadest sense, and in particular its algebraic, geometric and dynamical aspects.”

Topology is a field of mathematics which was born in the nineteenth century and has to do with properties of surfaces that do not change when they are deformed. Topologically, a circle and a square are the same; similarly, surfaces of a doughnut and a coffee mug with one handle are topologically equivalent, however the surface of a sphere and a coffee mug are not equivalent.

Early influences

This mapping was what excited Dennis P. Sullivan when he was in the second year of a Chemical Engineering course at Rice University, Texas. “The epiphany for me was watching the professor explaining that any surface topologically like a balloon, and no matter what shape – a banana or the statue of David by Michelangelo could be placed on to a perfectly round sphere so that the stretching or squeezing. required at each and every point is the same in all directions at each such point,” he said. Further the correspondence was unique once the location of three points was specified and these points could be specified arbitrarily… “This was general , deep and absolutely beautiful,” he recalls. He at once changed his major to take up mathematics, which became his lifelong interest.

He was so struck by this concept that he used it in later research, especially during a 10-year struggle with a proving mathematically, by 1990, a numerical Universality discovered by physicists in the mid-1970s.

Changing the landscape, building bridges

“Dennis P. Sullivan has repeatedly changed the landscape of topology by introducing new concepts, proving landmark theorems, answering old conjectures and formulating new problems that have driven the field forwards,” says Hans Munthe-Kaas, chair of the Abel Committee, in a press release given by the Academy.

The release further says that Prof. Sullivan has found deep connections between a variety of areas of mathematics. One of his key breakthroughs is in developing a new way of understanding rational homotopy theory, a subfield of algebraic topology. Later, in the late 1970s, he started working on dynamical systems, a field considered far removed from algebraic topology. Dynamical systems is the study of a point moving in geometrical space.

In 1999, he and his wife and collaborator, Moira Chas, discovered a new invariant for a manifold based on loops, creating the field of string topology.

Dennis P. Sullivan has won numerous awards, among them the Steele Prize, the 2010 Wolf Prize in Mathematics and the 2014 Balzan Prize for Mathematics. He is also a fellow of the American Mathematical Society.