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Dennis Parnell Sullivan Awarded the 2022 Abel Prize for Mathematics

Dennis sullivan feature
Dennis sullivan torus
Dennis Parnell Sullivan was awarded the 2022 Abel Prize for Mathematics. Photos by John Griffin.

Dennis Parnell Sullivan, distinguished professor in the College of Arts and Sciences Department of Mathematics, and the Albert Einstein Chair in Science (Mathematics) at the CUNY Graduate Center, is the recipient of the 2022 Abel Prize for Mathematics.

Awarded by the Norwegian Academy of Science and Letters “for his groundbreaking contributions to topology in its broadest sense, and in particular its algebraic, geometric and dynamical aspects,” Sullivan will receive an award of 7.5 million Norwegian kroner (nearly US $860,000), funded by the Norwegian government.

“This prize honors brilliant mathematicians who inspire curiosity and drive imagination. Who better to receive this tremendous recognition than distinguished professor Dennis Sullivan,” said Maurie McInnis, president of Stony Brook University. “Professor Sullivan has made outstanding scientific contributions to the field of mathematics, and we are very proud of the impact he has made throughout his illustrious career, especially on those he has mentored. We are so fortunate to have him among our esteemed colleagues, and all of Stony Brook joins me in offering congratulations for receiving such a prestigious prize.”

Throughout his decades-long career as a mathematician, Sullivan has found deep connections between many areas of mathematics. One of his most important breakthroughs includes a new way of understanding rational homotopy theory, a subfield of algebraic topology. Topology has been invaluable throughout mathematics and beyond, with significant applications in fields ranging from physics to economics to data science.

“Professor Sullivan is an extraordinary mathematician, and we are extremely proud of his fundamental contributions to topology and dynamical systems,” said Mónica Bugallo, interim provost for Stony Brook University. “The Abel Prize is one of the most prestigious in the field of mathematics and undoubtedly, he is more than deserving of this accolade. This recognition is a further confirmation of the status of our mathematics department as a world-class group of scholars.”

In the late 1970s, Sullivan began to work on problems in dynamical systems — the study of a point moving in a geometrical space — a field usually considered far removed from algebraic topology. The ability of computers to iterate functions beyond what was humanly possible had created an explosion of interest in this field, known popularly as “chaos theory,” since many of the dynamical systems exhibited chaotic behavior. Among Sullivan’s most important contributions to this field is the proof of the universality law for period doubling for a large class of dynamical systems.

“We are all thrilled for our colleague and friend Dennis Sullivan to be named this year’s recipient of the Abel Prize,” said Alexander Kirillov, professor and chair, Department of Mathematics. “The breadth of his mathematical results — from algebraic topology, in which he made groundbreaking discoveries, to fluid dynamics — is astonishing. One of the most accomplished mathematicians of our age, Dennis approaches mathematics with the enthusiasm and curiosity of a child first realizing the wonders of this incredible field. He has shared his passion for mathematics with generations of students and colleagues, and we are very fortunate to have him as a colleague in our department.”

Dennis sullivan head

Among Sullivan’s significant results in topology is his proof of the Adams conjecture, and in dynamical systems, he proved that rational maps have no wandering domains, solving a 60-year-old conjecture. His insistent probing for fundamental understanding and his capacity to see analogues between diverse areas of mathematics, and build bridges between them, has forever changed the field.

“Professor Dennis Sullivan has been an esteemed member of the Graduate Center’s faculty for more than 40 years. His pioneering discoveries in topology and dynamical systems, along with his mentorship of students, have been great gifts to mathematicians worldwide,” said Robin L. Garrell, president of the CUNY Graduate Center. “The Abel Prize is a well-earned recognition of his extraordinary achievements and impact. He has not only solved problems, he has opened new avenues of research that scholars will explore for years to come.”

In 1999 Sullivan and Moira Chas, associate professor in the Department of Mathematics, discovered a new invariant for a manifold based on loops, creating the field of string topology, an area that has grown rapidly in recent years.

“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,” said Hans Munthe-Kaas, chair of the international Abel prize committee. “Sullivan has moved from area to area, seemingly effortlessly, using algebraic, analytic and geometric ideas like a true virtuoso.”

Sullivan received his PhD in 1966 from Princeton University. That same year, he was awarded a NATO Fellowship at Warwick University in England, after which he earned a Miller Fellowship at the University of California at Berkeley (1967-69), and went to the Massachusetts Institute of Technology as The Sloan Fellow of Mathematics (1969-73).

Sullivan spent the 1973-74 academic year in France as professeur associé at the University of Paris-Orsay and became in 1974 a permanent professor at the Institut des Hautes Études Scientifiques. In 1981 he was appointed to the Albert Einstein Chair in Science (Mathematics) at the CUNY Graduate Center, a role that continues to this day, and worked jointly with the Institut des Hautes Études Scientifiques until 1996. He joined the faculty of the Department of Mathematics at Stony Brook University in 1996.

Dennis sullivan class

He was elected a member of the U.S. National Academy of Sciences (1983), corresponding member of the Brazilian National Academy of Sciences (1983), member of the New York Academy of Sciences (1984), fellow of the American Academy of Arts and Sciences (1991), corresponding member of the Irish Royal Society (2012), honorary member of the London Mathematical Society (2013) and served as vice president (1990-93) of the American Mathematical Society.

A recipient of numerous prestigious awards, Sullivan received the Oswald Veblen Prize in Geometry (1970), the Elie Cartan Prize in Geometry (1981), the King Faisal International Prize for Science (1994), the Gold Medal of the Brazilian Academy of Sciences (1996), the U.S. National Medal of Science (2004), the AMS Steele Prize for Lifetime Achievement (2006), the Wolf Prize in Mathematics (2010), and the Balzan Prize for Mathematics (2014).

Sullivan is the second Stony Brook faculty member to receive the Abel Prize. Laureate John Milnor, distinguished professor in the Department of Mathematics, was awarded in 2011.

The Abel Prize is named after Niels Henrik Abel, Norway’s greatest mathematician, who left lasting marks on the mathematical world. His mathematics have served as a base for a number of major technological breakthroughs, including the development of the internet. The Abel Prize was established by the Norwegian Parliament (The Storting) in 2002, on the 200th anniversary of Abel’s birth. The choice of the Abel laureate is based on the recommendation of the Abel Committee, which is composed of five internationally recognized mathematicians. The Norwegian Academy of Science and Letters, on behalf of the Ministry of Education, awards the Prize.

His Majesty King Harald will officially present the Prize at a ceremony in Oslo, Norway, on May 24. Watch the 2022 Abel Prize announcement here.

— Rachel Rodriguez

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