2022 Abel Prize Goes to New York Mathematician


Dennis P. Sullivan, professor of mathematics at Stony Brook University and the City University of New York Graduate Center, won this year’s Abel Prize, the equivalent of the Nobel in mathematics.

In a quote from the Norwegian Academy of Sciences and Letters, the organization that manages Abel, Dr. He said Sullivan was honored “for his groundbreaking contributions to topology in its broadest sense, and particularly in its algebraic, geometric and dynamical aspects.”

Topology is the study of space and shapes, and Dr. Much of Sullivan’s work includes higher-dimensional versions of two-dimensional surfaces, which mathematicians call manifolds. While this work is abstract, some of his latest research on fluid flows and turbulence may contribute to an understanding of the paths of hurricanes, the distributions of air pollutants, and the eddies behind airplane wings.

There are no Nobel Prizes in mathematics, and for decades the most prestigious awards in mathematics have been the Fields Medals, awarded in small groups every four years to the most accomplished mathematicians aged 40 and under.

Abel, named after a Norwegian mathematician, Niels Henrik Abel, was founded more like the Nobels. It has been given annually since 2003 to highlight important developments in mathematics. Previous award winners include Andrew J. Wiles, Who proved Fermat’s last theorem? and now at Oxford University; John F. Nash Jr.His life was portrayed in the movie “A Beautiful Mind”; and Karen UhlenbeckShe is a professor emeritus at the University of Texas at Austin who became the first woman to receive an Abel in 2019.

Ulrike Tillmann, a mathematician from the University of Oxford who served on the Abel committee, told Dr. Given Sullivan’s “absolutely great work” in both algebraic topology and dynamical systems, “it was a very easy decision to make,” he said.

Dr. Sullivan said she had a “nice response” to the news.

“I’m 81 years old,” he said. “They remember me.”

The award is accompanied by 7.5 million Norwegian crowns, or approximately $850,000.

Dr. Sullivan was born in Port Huron, Michigan in 1941; His family later moved to Houston.

In a parallel universe, Dr. Sullivan may have spent his career as a chemical engineer. This was his major at Rice University until his sophomore year. One day, during an advanced math class, the professor drew two shapes on the board—one with a circle, the other with more bubbles, like a kidney. He said you can then stretch one to fit the other.

This was not particularly surprising. But then the professor said there was a way to stretch the stretch to be the same in all directions, and it was essentially the only way.

“This blew my mind,” Dr. sullivan “This was not like the math I was learning up to that point. It was much deeper.”

He moved from chemical engineering to mathematics and earned his PhD at Princeton in 1966.

Dr. Sullivan was one of the first to adopt a technique known as surgical theory. Using this method allowed innovative mathematical discoveries, such as drilling two round holes in a sphere and then sticking one end of a tube into each hole outside the sphere, producing a kettleball-like shape.

This allowed mathematicians to examine what types of topologies could be put together.

Sullivan used the theory of surgery to examine how manifolds can be broken down into simpler parts: For example, a two-dimensional manifold, such as the surface of a sphere, can be approximated by triangles that are then glued back together.

It was known that all triangulations of two-dimensional surfaces were equivalent, and the same was true for three-dimensional manifolds.

The claim was assumed to be true for manifolds of all dimensions, and Dr. Sullivan showed that this is almost always true in five dimensions or more.

It turns out that there are a few exceptions where two triangulations of a five-dimensional manifold are not equivalent. Other mathematicians later showed that the conjecture is not true for many four-dimensional manifolds.

Later, Dr. Sullivan shifted his focus to dynamical systems, but these issues still contained many facets. “Dynamic systems happen inside manifolds,” he said. “It’s a way of returning to the geometric context.”

One of his enduring contributions is what is known as the “Sullivan dictionary”, which combines dynamics with three-dimensional geometry. This allowed him to prove a mathematical conjecture that had not been solved since the 1920s.

The deep and unexpected connections between these disciplines, Dr. It also helped Sullivan find the mathematical underpinnings for a phenomenon known as period doubling, which had been discovered and studied by physicists.

It was not an easy problem. “You had to find the hypothesis that got it right,” Sullivan said. “It took eight years.”

Dr. “It started a whole new theory of complex dynamical systems,” said Harvard mathematician Curtis T. McMullen, who completed his graduate studies as Sullivan’s advisor. “The tools he uses and, more importantly, the similes he highlights have guided the field ever since.”

Dr. Sullivan has since also solved problems in fluid dynamics.

When Sullivan accepted the Balzan Mathematics Prize in 2014, he said he hoped to test whether the theoretical tools he developed could be applied to practical problems such as hurricane prediction and the air resistance of airplane wings.

Dr. Sullivan said he can’t yet show he’s found better computer models. But I can say that we are on the right track,” he said.



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