# The prize is about 5.75 million yuan, and the “Nobel Prize” in mathematics is awarded to topology master Sullivan

Source: Science Network

At 7 p.m. Beijing time on March 23, the Abel prize, known as the “Nobel Prize” in mathematics, was announced. The Norwegian Academy of science and arts decided to award the 2022 Abel award to Dennis Parnell Sullivan of the State University of New York at Stony Brook in recognition of his outstanding achievements in “pioneering contributions to topology in the broadest sense, especially in algebra, geometry and dynamics”.

The Abel prize was established in January 2002 and first awarded on June 3, 2003. One of its original intentions was to make up for the lack of Nobel Prize in mathematics. The prize was NOK 7.5 million (about RMB 5.75 million). The award, together with the fields award and the Wolff mathematics award, is known as the “three awards” in the international mathematics community.

Hans Munthe Kaas, chairman of the Abel prize committee, said: “Dennis Sullivan has continuously promoted the development of topology by introducing new concepts, proving landmark theorems, answering old conjectures and constructing new problems to promote the development of this field”.

In Hans Cass’s view, “Dennis Sullivan is a real master who seems to transform different fields of mathematics effortlessly using algebraic, analytical and geometric ideas.”

Dennis Sullivan is an American mathematician. He is now an academician of the National Academy of Sciences, the New York Academy of Sciences and the American Academy of Arts and Sciences. Its most famous achievement is the pioneering research in topology and dynamical system, which are at the core of geometric structure theory. As a member with extraordinary charm and vitality in the field of mathematics, Sullivan found the deep connection between various fields of mathematics& nbsp;

Unremitting exploration and building a bridge between mathematics

It was born in the late 19th century. It is a new method of qualitative geometry.

Topology studies the properties of geometry or space that will not change after continuously changing the shape, that is, it only considers the positional relationship between objects without considering their shape and size. For example, a circle is the same as a square, while the surface of a sphere is different from that of a doughnut. Topology has irreplaceable value in mathematics and other fields, especially in the fields of physics, economics and data science.

Sullivan was born in Port Huron, Michigan on February 12, 1941. When he was young, he moved with his family to Houston, Texas. He studied at Rice University. He first studied chemistry and soon transferred to mathematics.

After graduating from university in 1963, Sullivan entered Princeton University for postgraduate study and started topology research. He was tutored by William Browder & nbsp; （William Browder） And Sergei Novikov & nbsp; （Sergei Novikov） Based on the research results of, this paper studies one of the most basic problems in topology – the classification of manifolds.

In the third year of his PhD, Sullivan completed his doctoral thesis “trigonometric homotopy equivalence”. He formed an algebraic topology view on this problem and put forward some ingenious methods to solve the problem. Including the concept of “positioning of space at a prime number” and “complementation of space at a prime number”. These ideas are derived from pure algebra, which can provide a new language for expressing geometric phenomena and become a tool to solve many problems.

In his fourth year, Sullivan completed a paper on the important conjecture “hauptvermutung” in geometric topology. In 1971, with this achievement, he won the “Veblen geometry Award” issued by the American Mathematical Society, which was Sullivan’s first award in his career.

After receiving his doctorate, Sullivan won scholarships from the University of Warwick in the UK, the University of Berkeley in the United States and the Massachusetts Institute of technology. He also became a “Sloan scholar” (the Sloan Foundation rewards outstanding scientists and scholars in the early stage of their career).

During this period, Sullivan put forward new theories and established a new vocabulary, which gradually changed the way mathematicians thought about algebra and geometric topology. In 1970, he completed a complete set of notes “MIT notes”, but it was not published at that time, but it was widely circulated, and even directly affected the classification of smooth manifolds and the core problems in algebraic topology, which is considered to have great influence. Finally, the note was published in 2006.

In 1974, Sullivan became a lifelong professor at the French Institute of higher sciences. Here, he completed the most important breakthrough – he found a new method to understand algebraic topological subdomains, “rational homotopy”. This method is based on a concept of differential form multivariable calculus, which can be directly connected with geometry and analysis, which makes the main part of algebraic topology suitable for calculation and makes the calculation easier. This method has been proved to be a breakthrough.

In the late 1970s, Sullivan began to study the problems in dynamical systems, that is, the motion of points in geometric space, which is far from algebraic topology. In 1985, Sullivan proved that rational mapping had no wandering region and solved the fatu conjecture 60 years ago, which was another milestone in his career.

In 1997, Sullivan left France and returned to the United States to become a professor at the State University of New York at Stony Brook. He also returned to topology academically. He and mathematician Moira Chas discovered a new class of loop based topological invariants of manifolds, thus opening up an independent new field of “string topology”. “String topology” is considered to be the beginning of understanding quantum field theory in mathematics, mainly in algebra, and has developed rapidly in recent years.

In 2008, Sullivan, together with hedge fund billionaire and philanthropist Jim Simmons, published a paper entitled “axiomatic characteristics of general cohomology of differential forms” in the Journal of topology.

Sullivan made unremitting exploration on the cognition of basic science, keenly found the similarities between different fields of mathematics, built a bridge between them, and forever changed the research of topology.

Sullivan’s outstanding achievements in mathematics have won numerous awards. In 1974, he was invited to give a report at the International Conference of mathematicians, an honor awarded to the top mathematicians in his field. His famous awards include the first Ellie gardang award of the French Academy, King Faisal International Science Award, American National Science Award, stile lifetime achievement award of the American Mathematical Society, Balzan mathematics award, wolf award, etc.

Sullivan now has six children, one of whom inherited his mantle and became a mathematician.

Author Han Yangmei

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