Reports from the Heart of the Machine
Editors: Du Wei, Chen Ping
The 81-year-old just had his birthday last month, and the Abel Prize was his "belated birthday present."
On the evening of March 23, Beijing time, the Norwegian Academy of Sciences and Letters announced the winners of the 2022 Abel Award, the Distinguished Professor of the State University of New York at Stony Brook, the Graduate School of the City University of New York and the University Center Albert M. Einstein Chair Professor Dennis M. Dennis Parnell Sullivan "recognizes his pioneering contributions to topology in the broadest sense, particularly in algebra, geometry, and dynamics."
The Abel Prize is named after the Norwegian mathematician Niels Hendrik Abel. Since 2003, the prize has been awarded annually to people who have made a significant impact on the mathematical community, and together with the Wolf Prize and the Fields Medal, it has been hailed as the "three major awards" in the mathematical community. The prize is NOK 7.5 million (about MORE THAN 5.5 million RMB).
After the secretary-general of the Norwegian Academy of Sciences and Letters informed him of the award, the 81-year-old man played a bit of humor, "Thank you for the good news, 9 a.m. looks a little suspicious."
Image source: https://www.youtube.com/watch?v=n-hlpn86U20
Sullivan Profile
Sullivan was an American mathematician with great achievements in topology and dynamical systems.
Sullivan was born on February 12, 1941 in Port Huron, Michigan, and moved with his family to Houston, Texas as a child. He then entered Rice University, initially studying chemistry, but soon switched to mathematics, graduating in 1963.
As a graduate student at Princeton University, Sullivan builds on the work of his dissertation advisors William Browder and Sergei Novikov on manifold classification, one of the fundamental problems of topology. Sullivan's 1966 doctoral dissertation, Triangulating Homotopy Equivalences, developed the technique and provided insights to help revolutionize the field. The following year, Sullivan completed an important conjecture on geometric topology, the Hauptvermutung paper, and was awarded the Oswald A. Varten paper by the American Mathematical Society in 1971. The Veblen Prize in Geometry, the first award he received in his career.
After receiving his Ph.D., Sullivan was awarded fellowships from the University of Warwick (1966–67), Berkeley (1967–69) and MIT (1969–73), as well as a Sloan Scholar.
During this time, Sullivan gradually changed the way mathematicians thought about algebra and geometric topology, introducing new ideas and establishing new vocabularies. In 1970, he completed a set of notes, MIT Notes, which were not published until 2006, but were widely disseminated and influential, directly influencing the core problems in smooth manifold classification and algebraic topology. At the 1974 International Congress of Mathematicians, Sullivan was invited to give a lecture, an honor awarded to top mathematicians. He taught at the University of Paris-Orsay in Paris from 1973 to 1974 and subsequently became a tenured professor at the French Institute for Higher Studies (IHES) near Paris.
An important breakthrough made
While in France, Sullivan made one of his most important breakthroughs—a new way of understanding rational homotopy theory, a subfield of algebraic topology.
Back in 1969, Daniel Daniel Quillen introduced the field from an algebraic perspective. But Sullivan's work used a concept of multivariate calculus, the differential form, which opened up the theoretical field and made computation easier.
In 1981, Sullivan was appointed to the Albert M. Miller Institute of the Graduate School and University Center of the City University of New York. Einstein Chair Professor of Mathematics and still retained the position at the Institute of Higher Scientific Studies in France.
dynamical system
By the late 1970s, Sullivan began to study problems in dynamical systems, namely moving points in geometric space. This field is often considered to be far removed from algebraic topology. The ability of computers to iterate over functions is beyond human reach, thus stimulating great interest in the field, and because many dynamical systems exhibit chaotic behavior, the famous "chaos theory" has emerged.
One of the most famous images in the powertrain is a bifurcation chart, in which one line is repeatedly split into two lines in a distinctly confusing way. American mathematical physicist Mitchell Mitchell Feigenbaum found in these graphs some ratios that apply to all systems. In 1988, Sullivan gave a proof of concept for this universality.
A bifurcation diagram of a logistic map. Image source: Wikipedia
Discover new invariants
Sullivan left the Institute for Higher Studies in France in 1997 to become a professor at the State University of New York at Stony Brook, returning academically to topology. In 1999, Sullivan and mathematician Moira Chas discovered new invariants based on manifolds, pioneering string topology, a field that has grown rapidly in recent years.
Moira Chas, a mathematician at the State University of New York at Stony Brook and wife of Sullivan.
Awards won
Sullivan's notable awards include the following:
In 1981 the first Elie of the Institut de France Lie Cartan Prize
King Faisal International Prize in Science, 1993
USA's National Medal of Science 2005
2006 AMS Steele Prize for Lifetime Achievement
Wolf Prize 2010
2014 Balzan Prize for Mathematics
In addition, Sullivan was a fellow of the National Academy of Sciences, the New York Academy of Sciences, and the American Academy of Arts and Sciences, and was vice president of the American Mathematical Society from 1990 to 1993.
Reference link: https://abelprize.no/biography/biography-dennis-p-sullivan